Xu,
Your EMA question is related to algorithms for linear recurrence
relations. There is a much loved algorithm (probably because it's
usually found to be lean and mean) that I first encountered at IP
Sharp in a newsletter quiz. We used it all over the place,
particularly wherever a present value or discounted cash flow was in
play. Where it came from before that, I know not. It goes like this.
If you have a linear recurrence relation of the form:
r[0] is m[0] times a[0]
r[i] is a[i] + m[i] times r[i-1] (i >0)
then this can be calculated in vector languages in the following way:
a recur m;t
t is timesscan m
r is t times plusscan a div t
I'd be most interested to see a J algorithm for this, particularly a
tacit one. I note that we have a reflexive piece (t) and that there
may be an opportunity for an inverse (* and %).
As far as the EMA is concerned, I suggest Xu's original requirement is
solved with:
(y[0] , k times 1 drop y) recur (length y) replicate 1 - k
Mike Powell
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