JOLI - Julia Operators LIbrary

[REFERENCE guide] [Tutorials]

Julia framework for constructing matrix-free linear operators with explicit domain/range type control and applying them in basic algebraic matrix-vector operations.

Julia Operator LIbrary (JOLI) is a package for creating algebraic operators (currently linear only) and use them in a way that tries to mimic the mathematical formulas of basics algebra.

The package was created in SLIM group at the University of British Columbia for their work in seismic imaging and modelling.

JOLI has a collection of methods that allow creating and use of element-free operators, operators created from explicit Matrices, and composing all of those into complex formulas that are not explicitly executed until they act on the Vector or Matrix. '*', '+', '-', and etc... operations are supported in any mathematically valid combination of operators and vectors as long as vector is on the right side of the operator. Composite operators can be defined before they are used to act on vectors.

JOLI operators support operations like adjoint, transpose, and conjugate for element-free operators provided that enough functionality is provided when constructing JOLI operator.

JOLI operators support and enforce consistency of domain and range data types for operators with both vectors acted upon and created by operators. JOLI also has the functionality that allows easily to switch precision of computations using global type definitions.

Contrary to other linear-operators Julia packages, JOLI operators act on matrices as if those were column-wise collections of vectors. I.e. JOLI operator does not treat explicit matrix on left side of '*' as another operator, and will act on it immediately. Such behaviour is convenient for implementation of Kronecker product.

JOLI is registered and can be added like any standard julia package with the command:

] add JOLI

• CurveLab: In order to use joCurvelet2D or joCurvelet2DnoFFT operators, you need to obtain CurveLab-2.1.2-SLIM, a SLIM extension to CurveLab-2.1.2. The tarball of this extension is available from curvelet.org under Software tab. The installation instructions are included in the tarball of CurveLab-2.1.2-SLIM. Note, that CurveLab is free only for academic use and requires registration.

• PyWavelets: In order to use joSWT that implements 1D stationary/shift invariant wavelet transform, the PyWavelets package needs to be installed within the python environement used by PyCall.jl. By default, it will use Conda.jl and you should follow its directiv to install a package within it. If you have configured PyCall with your own python environment you can install PyWavelets via pip install --upgrade PyWavelets.

• REFERENCE guide.
• Tutorials

Check examples for the examples of how to build your own operators or types, or look up DCT implementation in src/joLinearFunctionConstructors/joDCT.jl.

Try templates/joLinearFunctionFwd.jl as a starting point for building your own operators.