Tools for building spectral methods

## Project description

The SpectralToolbox is a collection of tools useful for spectral approximation methods in one or more dimensions. It include the construction of traditional orthogonal polynomials. Additionally one can construct orthogonal polynomials with respect to a selected measure.

## Description

Implementation of Spectral Methods in N dimension.

Available polynomials:
• Jacobi
• Hermite Physicist
• Hermite Function
• Hermite Probabilistic
• Laguerre Polynomial
• Laguerre Function
• ORTHPOL package (generation of recursion coefficients using [1])
Available quadrature rules (related to selected polynomials):
• Gauss
• Gauss-Lobatto
Available quadrature rules (without polynomial selection):
• Kronrod-Patterson on the real line
• Kronrod-Patterson uniform
• Clenshaw-Curtis
• Fejer’s

## Installation

For everything to go smooth, I suggest that you first install some dependencies separately: numpy, scipy, matplotlib can be installed by:

\$ pip install numpy scipy matplotlib

If you want to accelerate some of the functionalities and work with orthogonal polynomials with respect to arbitrary measures, you should intall the orthpol package. This dependency is optional. The installation might require you to tweak some flags for the compiler (with gcc nothing should be needed).

\$ pip install orthpol

Finally you can install the toolbox by:

\$ pip install SpectralToolbox

## References

 [1] Gautschi, “Algorithm 726: ORTHPOL – a package of routines for generating orthogonal polynomials and Gauss-type quadrature rules”. ACM Trans. Math. Softw., vol. 20, issue 1, pp. 21-62, 1994

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