Which Krylov package solves A*x=b where x and b can be any "vector-like" object?

New to Julia
1

Hi, I would like to solve a linear equation Ax=b with Krylov method. My unknown “vector” x is a multidimensional array wrapped in a custom type that <:AbstractArray, and my A operator is just a linear map defined on x. Since x is not a AbstractVector, the linsolve function from KrylovKit does not seem to work: e.g.,

julia> using KrylovKit
julia> b=rand(3,3)
3×3 Matrix{Float64}:
 0.132235  0.562757  0.258504
 0.745966  0.236753  0.783062
 0.674764  0.8032    0.723963

julia> res = linsolve(b) do x
       return transpose(x)
       end
ERROR: MethodError: no method matching orthogonalize!(::LinearAlgebra.Transpose{Float64, Matrix{Float64}}, ::KrylovKit.OrthonormalBasis{Matrix{Float64}}, ::SubArray{Float64, 1, Vector{Float64}, Tuple{UnitRange{Int64}}, true}, ::ModifiedGramSchmidt2)

Here b is a 2D array not a vector, linsolve does not seem to like it.
So is there a general Krylov package that can solve this toy problem without explicitly “vectorize” inputs and outputs of the linear map?

2

IIUC, this is searching for f(X) = b, where b is not vector-like, but rather a Matrix.

Either try to define the missing orthogonalize! method for your output type,
or convert to a regular array (the collect used below) ?

julia> using KrylovKit
julia> b = rand(3, 3)
julia> res, info  = linsolve(b) do x
              return transpose(x) |> collect
       end;
julia> transpose(res) ≈ b
true
1 Like