[Python-ideas] [RFC] draft PEP: Dedicated infix operators for matrix multiplication and matrix power

[Steven D'Aprano]

On Sat, Mar 15, 2014 at 12:27:33PM +0100, Antoine Pitrou wrote:

> The real question is why @ would be right-associative.

That's a good question, but I don't think that should be up to us to 
decide. Guido clearly stated that if it is more useful to define @ as 
right-associative, we shouldn't let the fact that most operators are 
left-associative get in the way of doing the right thing here. The only 
people who are in a position to decide that are the users of matrix 
multiplication.


[...]
> The possible reason given in the PEP is very weak and amounts to
> premature optimization:

I don't think it's premature optimization. Sometimes we do know ahead of 
time that a calculation done one way will be faster than doing it 
another way: you don't have to "try it and see" to realise that 
repeatedly adding strings in a for-loop can be O(N**2) versus O(N) for 
using str.join(). [Aside: if you do try it, the string-concat 
reference-counting optimization of CPython may fool you into thinking 
that concatenation is generally fast. It isn't.]

Likewise there is nothing premature about the fact that "Matrix-vector 
multiplication is much cheaper than matrix-matrix multiplication". The 
only question is whether it is more common to write:

    Matrix @ Matrix @ Column_Vector

or

    Row_Vector @ Matrix @ Matrix


I'll leave it to those who do matrix maths to decide which they use more 
often, but personally I've never come across the second case except in 
schoolbook exercises.


> """It's been suggested that @ should be right-associative, on the
> grounds that for expressions like Mat @ Mat @ vec, the two different
> evaluation orders produce the same result, but the right-associative
> order Mat @ (Mat @ vec) will be faster and use less memory than the
> left-associative order (Mat @ Mat) @ vec. (Matrix-vector multiplication
> is much cheaper than matrix-matrix multiplication)."""
> 
> If that's the only reason, then I'd like @ to be left-associative.

I'm not sure that premature pessimation is much of an improvement over 
premature optimization.

*wink*



-- 
Steven