[ruby-core:28402] Re: [Feature #2772] Matrix: Calculating determinant using Bareiss algorithm [patch]

Hi,

On Sat, Feb 20, 2010 at 9:08 PM, Yu Ichino <[e-mail]> wrote:
> After my initial post,
> I came to conclude that the slower performance in the Float case
> is due to additional multiplication a[k][k]*a[i][j]
> and is unavoidable.
> Am I correct?

Yes, there is one that additional term in the inner loop, and a division too.

> If so,
> you better keep the original algorithm for Float matrix
> (still I don't get the reason of many swap operations)
> and use Bareiss only for Integer one.
> It depends on the library policy of which I am completely ignorant.
> (Matrix#determinant might be the only interface users want to see)

We could scan the matrix and pick the algorithm in function of the
presence of non-integer elements or not (see redmine:2831). This keeps
the complexity the same. There is still a huge gain for Integer
matrices, and for most float matrices there will be no loss of
performance at all (since in most of these cases all elements are
floats and thus the check will return after inspecting the first
element).