spectraltoolbox 0.2.22

Tools for building spectral methods

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 Physicists’

• Hermite Physicists’ Function

• Hermite Probabilists’

• Hermite Probabilists’ Function

• Laguerre Polynomial

• Laguerre Function

• Fourier

• ORTHPOL package (generation of recursion coefficients using [1])

Available quadrature rules (related to selected polynomials):

• Gauss

• Gauss-Lobatto

• Gauss-Radau

Available quadrature rules (without polynomial selection):

• Kronrod-Patterson on the real line

• Kronrod-Patterson uniform

• Clenshaw-Curtis

• Fejer’s

Requirements

• numpy

• scipy

• orthpol >= 0.2.2

Installation (using pip)

For everything to go smooth, I suggest that you first install the requirements separately, even if in some environments the direct installation of SpectralToolbox should work.

$ pip install numpy

$ pip install scipy

$ pip install Sphinx

$ pip install sphinxcontrib-bibtex

You should intall the orthpol package. This dependency is required since v. 0.2.0. The installation might require you to tweak some flags for the compiler (with gcc nothing should be needed).

$ pip install –install-option=”install” orthpol

Finally you can install the toolbox by:

$ pip install SpectralToolbox

Installation (using Anaconda)

There is no anaconda package right now, so the dependencies and the installation must be carried out manually. First resolve some of the dependencies through conda:

$ conda install pip

$ conda install numpy

$ conda install scipy

Resolve the remaining dependencies manually:

$ cd <download_dir>

$ pip install -d ./ <package>

$ tar xzf <package>-X.X.X.tar.gz

$ cd <package>-X.X.X

$ python setup.py install

where <package> are in sequence: orthpol, SpectralToolbox.

References

[1]

23. 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

Change Log

0.1.0:

• Implementation of Poly1D, PolyND, and additional quadrature rules

0.2.0:

• New interface for Spectral1D.

• All polynomials are now classes.

• Complete integration of orthpol

0.2.7:

• Python3 support. And fixed installation procedure.

0.2.8:

• Bug fix from orthpol package

0.2.11:

• Added function generate for the generation of polynomials from type and parameters.