Add support for block Topelitz matrices

[imciner2]

Many applications (such as MIMO control, filtering, etc.) have block Topelitz matrices involved. Currently, this library only seems to support scalar Toeplitz matrices, so it would be nice to extend it to handle block Toeplitz matrices (both generic blocks and block-Toeplitz-Toeplitz-block matrices).

[dlfivefifty]

Great idea. Note that it should build on BlockArrays.jl

FYI There is experimental implementation of infinite dimensional block Toeplitz operators in InfiniteLinearAlgebra.jl.

[ignace-computing]

Can you please help me a bit implementing this? I am correct in saying that a user interface could look like this, for instance:

a = mortar(reshape([randn(2,2), randn(2,2), randn(2,2)],3,1))
Toeplitz(a,a)
ERROR: MethodError: no method matching Toeplitz(::BlockMatrix{Float64, Matrix{Matrix{Float64}}, Tuple{BlockedUnitRange{Vector{Int64}}, BlockedUnitRange{Vector{Int64}}}}, ::BlockMatrix{Float64, Matrix{Matrix{Float64}}, Tuple{BlockedUnitRange{Vector{Int64}}, BlockedUnitRange{Vector{Int64}}}})
Closest candidates are:
  Toeplitz(::AbstractMatrix) at ~/.julia/packages/ToeplitzMatrices/eInzd/src/toeplitz.jl:38
Stacktrace:
 [1] top-level scope
   @ REPL[52]:1

However I am not sure where I should go to modify ToeplitzMatrices.jl. Any idea on how the above error can be solved? Also, presumably the function getindex should be changed so that it uses BlockArrays' indexing functions (e.g. aa[Block(1)])? Thank you, in advance!

[dlfivefifty]

It would probably go in a separate package BlockToeplitzMatrices.jl. Unfortunately I don't have time to help with this at the moment.