If the creation of the matrix is really slow, you could try this:
gensymm =: 1 : 0
NB. Create indexes to produce a 2xn array of items that make up the lower
triangle
insel =. ;@:(<@(,. i.@>:)"0)@:i.@:#
NB. Get array of indexes, in the linear output, for each matrix position
outsel =. (-:@(* >:)@:>. + <.)"0 _~@:i.@:#
outsel f. { [: u/"(1 + u b. 0) insel f. { ]
)
+ gensymm i. 5
0 1 2 3 4
1 2 3 4 5
2 3 4 5 6
3 4 5 6 7
4 5 6 7 8
It selects the unique pairs of y, runs u, and then creates
a matrix of the results.
Henry Rich
> -----Original Message-----
> From: [EMAIL PROTECTED]
> [mailto:[EMAIL PROTECTED] On Behalf Of Fraser Jackson
> Sent: Saturday, September 02, 2006 6:34 AM
> To: Programming forum
> Subject: Re: [Jprogramming] Symmetric inner and outer products
>
> 1. My initial question raised a simple and very common
> computational
> structure which seemed to me to offer a reasonably simply attainable
> improvement. Since the calculations expand O(*:n) halving it
> helps at least
> a little. It has been considered before. I just wanted it
> considered again
> in case its relative position in the wish list might have improved.
>
> 2. The problem was not matrix multiplication. If the
> function f in f"1
> 1/~ is itself quite slow, a factor of 2 can be very helpful
>
> 3. Henry's point that you then have to use the matrix is
> germane. In
> some cases that is very complex. In my problem, it is very
> simple and fast.
>
> 4. I am not in a position comment on the strategic issues
> which Henry and
> Bill raised, but handling multiple cores and taking
> advantage of changes in
> the instruction set on the most recent chips sound as if they
> will give much
> value to the J community. I have no idea of how big a task that is.
>
> 5. Roger has often made the point that the core language
> should be kept
> as simple and powerful as possible and where the user has
> something beyond
> that there have to be very good reasons for incorporating it.
> I do not think
> a factor of 2 on a very significant proportion of matrix
> operations is
> something which should be passed up. If it is to be
> considered further
> whether it uses the inner product or table form might make a big
> difference to the range of applications. Roger has already
> woven a lot of
> his magic on both.
>
>
> ----- Original Message -----
> From: "bill lam" <[EMAIL PROTECTED]>
> To: "Programming forum" <[email protected]>
> Sent: Saturday, September 02, 2006 4:45 PM
> Subject: Re: [Jprogramming] Symmetric inner and outer products
>
>
> > Henry Rich wrote:
> >> For arithmetic operations in general, it would also be
> >> a much better use of coding time to take advantage of
> >> the SSE3 instructions. With careful coding there could
> >> be a severalfold increase in speed for +/ .* and a
> >> noticeable improvement for other floating-point arithmetics.
> >
> > I agree with Henry. From source code of J7, it appeared J
> did not make use
> > of
> > floating point stack for computation. Not sure this had
> been changed in
> > later
> > release. Given that SIMD (MMX SSE SSE2 3DNow) is almost
> available in
> > every
> > Intel/AMD CPU. Not making use of them in computational
> intensive program
> > like J
> > seems under-utilise the CPU's raw power.
> >
> > --
> > regards,
> > bill
> >
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>
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