bump minor version and update readme

Project.toml

@@ -1,7 +1,7 @@
 name = "KrylovKit"
 uuid = "0b1a1467-8014-51b9-945f-bf0ae24f4b77"
 authors = ["Jutho Haegeman"]
-version = "0.8.3"
+version = "0.9"
 
 [deps]
 LinearAlgebra = "37e2e46d-f89d-539d-b4ee-838fcccc9c8e"

README.md

@@ -31,43 +31,27 @@ to vectors.
 
 ## Release notes for the latest version
 
-### v0.7
-This version now depends on and uses [VectorInterface.jl](https://github.com/Jutho/VectorInterface.jl)
-to define the vector-like behavior of the input vectors, rather than some minimal set of
-methods from `Base` and `LinearAlgebra`. The advantage is that many more types from standard
-Julia are now supported out of the box, such as nested vectors or immutable objects such as
-tuples. For custom user types for which the old set of required methods was implemented, there
-are fallback definitions of the methods in VectorInferace.jl such that these types should still
-be supported, but this might result in warnings being printed. It is recommend to implement full
-support for at least the methods in VectorInterface without bang or with double bang, where the
-latter set of methods can use in-place mutation if your type supports this behavior.
-
-In particular, tuples are now supported:
-
-```julia
-julia> values, vectors, info = eigsolve(t -> cumsum(t) .+ 0.5 .* reverse(t), (1,0,0,0));
-
-julia> values
-4-element Vector{ComplexF64}:
-  2.5298897746721303 + 0.0im
-  0.7181879189193713 + 0.4653321688070444im
-  0.7181879189193713 - 0.4653321688070444im
-  0.03373438748912972 + 0.0im
-
-julia> vectors
-4-element Vector{NTuple{4, ComplexF64}}:
- (0.25302539267845964 + 0.0im, 0.322913174072047 + 0.0im, 0.48199234088257203 + 0.0im, 0.774201921982351 + 0.0im)
- (0.08084058845575778 + 0.46550907490257704im, 0.16361072959559492 - 0.20526827902633993im, -0.06286027036719286 - 0.6630573167350086im, -0.47879640378455346 - 0.18713670961291684im)
- (0.08084058845575778 - 0.46550907490257704im, 0.16361072959559492 + 0.20526827902633993im, -0.06286027036719286 + 0.6630573167350086im, -0.47879640378455346 + 0.18713670961291684im)
- (0.22573986355213632 + 0.0im, -0.5730667760748933 + 0.0im, 0.655989711683001 + 0.0im, -0.4362493350466509 + 0.0im)
-```
+### v0.9
+KrylovKit v0.9 adds to new sets of functionality:
+* The function `lssolve` can be used to solve linear least squares problems, i.e. problems of the form `x = argmin(norm(A*x - b))` 
+  for a given linear map `A` and vector `b`. Currently, only one algorithm is implemented, namely the LSMR algorithm
+  of Fong and Saunders.
+* There are now two new functions `reallinsolve` and `realeigsolve`, which are useful when using vectors with complex arithmetic,
+  but where the linear map (implemented as a function `f`) acts as a real linear map, meaning that it only satisfies
+  `f(α*x) = α*f(x)` when `α` is a real number. This occurs for example when computing the Jacobian of a complex function that is
+  not holomorphic, e.g. in the context of automatic differentation. This is implemented by simply wrapping the vector as `RealVec`,
+  which is a specific `InnerProductVec` type where the redefined inner product forgets about the imaginary part of the original
+  `inner` function, thereby effectively treating the vector as living in a real vector space. Furthermore, in this setting, only
+  real linear combinations of vectors are allowed, so that for the case of `eigsolve`, only real eigenvalues and eigenvectors are
+  computed. An error will be thrown if the requested list of eigenvalues contains complex eigenvalues. 
 
 ## 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
+*   `lssolve`: solve least squares problems
 *   `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
@@ -94,7 +78,8 @@ julia> import Pkg; Pkg.add("KrylovKit.jl")
 
 ## Project Status
 
-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.
+The package is tested against Julia `1.6`, the long-term stable release (1.10), the current stable release as well
+as nightly builds of the Julia `master` branch on Linux, macOS, and Windows 64-bit architecture and with `1` and `4` threads.
 
 ## Questions and Contributions