ufl team mailing list archive

[Pearu Peterson <pearu@xxxxxxxxx>]

Martin Sandve Alnæs wrote:

> That's one of the trivial examples in my previous email. A*B and A*v
> work out fine, but v*A and u*v would be invalid products in
> Matlab/linear algebra notation. If you write (with tensors) "u v", it
> (often, usually, always?) means outer(u, v). Translating from linear
> algebra notation to UFL tensor notation, "u v" is invalid, "u^T v" is
> dot(u,v) and "u v^T" is outer(u, v).
>
> "Paper notation" contains a lot of special cases that doesn't
> generalize, and would lead to a tangled mess of code. That's why we
> must make our own precise definitions, that are always well defined
> and translates well to code. And since we're dealing with tensor
> algebra, we must use tensor algebra as our basis and not linear
> algebra where they differ.

FYI, in sympycore we have the same problem with matrices
and there we have resolved it as follows (for details see 
http://code.google.com/p/sympycore/wiki/MatrixSupportIdeas):

0) currently vectors are represented as 1-column matrices
1) by default, `A * B` is matrix product.
2) matrices have attributes .A, .T, etc (`.T` would be `^T` in your 
case) that return "array", "transpose", etc *views* of matrices
and these views define what kind of multiplication will be used.

For example, `A.A * B` would be equivalent to elementwise multiplication
of matrices. `A.T * B` would be dot product of matrices.
Outer products could be modelled as `A.O * B`, for instance.

Regards,
Pearu