[Libre-soc-dev] complex numbers as matrices
Luke Kenneth Casson Leighton
lkcl at lkcl.net
Fri Jun 25 22:55:31 BST 2021
On 6/25/21, Hendrik Boom <hendrik at topoi.pooq.com> wrote:
> Representing a complex number as a matrix makes it into a 2x2 matrix of
> reals,
> That means more data manipulation for the same complex number.
double the amount, right?
however what if you had A as a 2x2 matrix (ab) and B as a 1x2 vector (ef)?
(a -b (e
b a) f)
result is
(ae - bf)
(eb + af)
where the original was....
A = a + bj
B = e + fj
so A*B = ae - bf + (af + be)j
and yes it's the same! awesome.
the reason that's awesome is because we have a REMAP schedule system
capable of doing matrix-vector multiplication.
and if we have a scheduler for 2x2 matrices, it is quite
straightforward to embed *that* schedule into a larger one that
performs batches of them to create FFTs.
the only slightly awkward thing is, that's now 4 nested for-loops.
have to see if there's space.
>
> And matrix inverse is hard to do right. There's a lot of numerical
> analysis on the subject,
> It turns out that just about any operation that can be elegantly written
> using a matrix inverse can better be done by a different algorithm
interesting. appreciated.
l.
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