[Numpy-discussion] [help needed] associativity and precedence of '@'

[Christophe Bal]

I'm not saying that Python choices are wrong, I'm just saying that if * is
elementwise product, then (A*B)@C <> A*(B at C) should imply to choose
different levels fro * and @.

By choosing A*B at C = (A*B)@C, that is a convention, we just say that a human
who want to calculate something like A*B at C*D at E@G*H*K will have to start
first with the elementwise products and then finish by the matrix product
that is to say this human will evaluate (A*B)@(C*D)@E@(G*H*K).

Maybe you should argue to calculate first the @-products but this will not
be a good choice if * is the product of a scalar with a matrix like in 2*A at 3
*B.

*On the other hand, if you calculate from left to right, there will be a
lot of isolate @-products to do instead of doing a single one. This will
not allow to use the very good group technic you have proposed.*

    1) If A*B at C*D at E@G*H*K = (A*B)@(C*D)@E@(G*H*K), you quickly evaluate
first X = A*B, Y = C*D and Z = G*H*K, and then you can do an efficient
@-product of X, Y and Z.

    2) If you calculate from left to right, you will do three @-products on
couple without having the possibility to choose the more efficient way to
evaluate the @-products.

Christophe BAL


PS1: // is an approximate calculation of the exact mathematical inversion,
so it is not really a counter example.


PS2: here is a second time my example showing that (A*B)@C <> A*(B at C).

*    [1 2]*
*A = [3 4]*

*    [5 6]*
*B = [7 8]*

*    [a d]*
*C = [b c]*

*(A*B)@C*
*=*
*[5  12]   [a d]*
*[21 32] @ [b c]*
*=*
*[5a+12b  5d+12c ]*
*[21a+32b 21d+32c]*

*A*(B at C)*
*=*
*[1 2]   [5a+6b 5d+6c]*
*[3 4] * [7a+8b 7d+8c]*
*=*
*[5a+6b   10d+12c]*
*[21a+24b 28d+32c]*
-------------- next part --------------
An HTML attachment was scrubbed...
URL: <http://mail.python.org/pipermail/numpy-discussion/attachments/20140318/78ee5797/attachment.html>