Al-Jabr: Interfaces for implicit linear operators

This package implements interfaces for implicit linear operators, those defined by function and callable instead of matrix. It is useful when the matrix reprensentation is not adequat, for instance

when the dimension is large,
when more efficient computation is available instead of basic matrix vector product,
when the vector interface is not easy to manipulate.

A typical example is the Discrete Fourier Transform that is a linear operator but available through the usual fft and ifft function.

The code is in early development stage, Pre-Alpha.

If you are having issues, please let me know

francois.orieux AT universite-paris-saclay.fr

Features

A base type LinOp that represent an operator A whose behaviour depends on the two methods forward for A·x, that apply A on a vector x, and adjoint for Aᴴ·x that apply the adjoint Aᴴ on a vector x.
Compatible with LinearOperator of scipy.
The base type LinOp comes with handy utilities like +, - or * interface for basic composition, or automatic timing of instance creation or methods call.
matvec, rmatvec, __call__, * and @ interfaces.
Instance of common linear operator like Identity, Diagonal, DFT or convolution.
Utilities functions like asmatrix or dottest.

Installation and documentation

The package is not actually on pypi but versionned, I recommend to use poetry and run in a terminal

poetry add  "git+https://github.com/forieux/aljabr.git"

or add

aljabr = {git = "https://github.com/forieux/aljabr.git", rev = "main"}

in the [tool.poetry.dependencies] section of your pyproject.toml.

aljabr depends on NumPy, SciPy, udft and PyWavelets.

License

The code is in the public domain.