Khatri-Rao product

[pierrejoyot]

Currently, the Kronecker product (kron(A) function) of a BlockMatrix does not take into account the block structure of the matrix.

For BlockMatrix, the classical definition of the Kronecker product is replaced by the Khatri–Rao product or the Tracy–Singh product (https://en.wikipedia.org/wiki/Kronecker_product).

I would find it very interesting to add these functions to your very useful library.

My implementation of the Khatri–Rao product:

function kron_khatri_rao(A::AbstractBlockMatrix, B::AbstractBlockMatrix)
    # https://en.wikipedia.org/wiki/Kronecker_product
    _Ablksize = blocksize(A)
    _Bblksize = blocksize(A)
    @assert _Ablksize == _Bblksize

    _kblk = []
    for _iblk in 1:_Ablksize[1]
        _kblk_j = []
        for _jblk in 1:_Ablksize[2]
            _Ablk = A[Block(_iblk, _jblk)]
            _Bblk = B[Block(_iblk, _jblk)]
            push!(_kblk_j, kron(_Ablk, _Bblk))
        end
        push!(_kblk, tuple(_kblk_j...))
    end
    mortar(_kblk...)
end

[dlfivefifty]

Would love a PR for this!

We should support both and have one be the default. Note also test that the special routines work with Array: these are treated as block arrays with one block, so it would be great to have a convenient way to create a block array for the kronecker product

[pierrejoyot]

Ok, I'm preparing a PR

[dlfivefifty]

This is done. We also have blockkron.