KrylovKit.jl

A Julia package collecting a number of Krylov-based algorithms for linear problems, singular value and eigenvalue problems and the application of functions of linear maps or operators to vectors.

Documentation	Build Status

Release notes for the latest version

• a new method geneigsolve for generalized eigenvalue problems A x = λ B x, with a single implementation for symmetric/hermitian problems with positive definite B, based on the Golub-Ye inverse free algorithm.

• a verbosity keyword that takes integer values to control the amount of information that is printed while the algorithm is running.

Overview

KrylovKit.jl accepts general functions or callable objects as linear maps, and general Julia objects with vector like behavior (as defined in the docs) as vectors.

The high level interface of KrylovKit is provided by the following functions:

• linsolve: solve linear systems
• eigsolve: find a few eigenvalues and corresponding eigenvectors
• geneigsolve: find a few generalized eigenvalues and corresponding vectors
• svdsolve: find a few singular values and corresponding left and right singular vectors
• exponentiate: apply the exponential of a linear map to a vector

Installation

KrylovKit.jl can be installed with the Julia package manager. From the Julia REPL, type ] to enter the Pkg REPL mode and run:

pkg> add KrylovKit

Or, equivalently, via the Pkg API:

julia> import Pkg; Pkg.add("KrylovKit.jl")

Documentation

• STABLE - documentation of the most recently tagged version.
• DEVEL - documentation of the in-development version.

Project Status

The package is tested against Julia 0.7, 1.0 and the nightly builds of the Julia master branch on Linux, macOS, and Windows.

Questions and Contributions

Contributions are very welcome, as are feature requests and suggestions. Please open an issue if you encounter any problems.