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.
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This version introduces (minimal) breaking changes, if you use KrylovKit.jl with custom
vector types: KrylovKit.jl no longer depends on eltype(::YourCustomVector) and
similar(::YourCustumVector, ::Type{<:Number}). Instead, KrylovKit.jl does now rely on
Base.:*(::Number, ::YourCustomVector) to be defined as a means of creating new vectors,
possibly with a different scalar type, so as to be able to represent this computation. Note
that Base.similar(::YourCustomVector) (without the second argument) should still be
defined to create uninitialized vectors of the same type as the one of the argument.
The motivation for this is that using eltype(::YourCustomVector) to represent its scalar
type, was often not the compatible with the requirements for Base.eltype if your type also
supports iteration or indexing.
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 systemseigsolve: find a few eigenvalues and corresponding eigenvectorsgeneigsolve: find a few generalized eigenvalues and corresponding vectorssvdsolve: find a few singular values and corresponding left and right singular vectorsexponentiate: apply the exponential of a linear map to a vectorexpintegrator: exponential integrator for a linear non-homogeneous ODE, computes a linear combination of theϕⱼfunctions which generalizeϕ₀(z) = exp(z).
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")- STABLE - documentation of the most recently tagged version.
- DEVEL - documentation of the in-development version.
The package is tested against Julia 1.0, the current stable and the nightly builds of the Julia master branch on Linux, macOS, and Windows, 32- and 64-bit architecture and with 1 and 4 threads.
Contributions are very welcome, as are feature requests and suggestions. Please open an issue if you encounter any problems.