[Gretl-devel] Re: Kronecker product and power

[Allin Cottrell]

On Thu, 1 Feb 2007, Riccardo (Jack) Lucchetti wrote:

> Unfortunately, the recent fixes to the matrix handling code broke the
> Kronecker product: if you try the following on CVS
>
> nulldata 2
> a = mnormal(2,2)
> b = mnormal(2,2)
> c = a ** b
>
> it gives an error. That is because the "**" is interpreted as B_POW
> instead of KRON.

Thanks for spotting that.  I have tried to work around the problem 
in this way:

(a) if we know in advance that we're generating a matrix we 
interpret "**" as KRON, and

(b) if in the evaluation phase we find that one or both of the 
operands of B_POW is a matrix, and if the B_POW was an 
interpretation of "**", we revise the interpretation to KRON.

> As a consequence, I propose a syntax change (and this is the 
> reason why I'm cc-ing the devel-list): reserve "^" for power and 
> "**" for the Kronecker product. I'm aware that this introduces 
> another breakage in backward-compatibility, but looks to me as 
> the only clean way out.

I see your point, but I don't want to break the old use of "**" if 
I can help it.

> for example, what would the intended result of
>
> C = A ** x
>
> be, if A is a matrix and x is a scalar?

The way I have things right now, this instance of "**" would 
produce an error: "Data types not conformable for operation". 
That's because the presence of A on the left means "**" will be 
interpreted as KRON, which requires two matrices as operands.

I _think_ that's fair enough, because although the main "genr" 
documentation says "**" is a synonym for "^", the matrix chapter 
of the guide says plainly to use "A^k" for raising a matrix to a 
power (and says "**" = Kronecker).

No, this is not perfectly clean -- but is it acceptable?

Allin.