https://en.wikipedia.org/wiki/Logarithmic_mean defines logarithmic
mean as the the limit of difference of two numbers divided by the
difference of their (natural) logs. The limit is to deal with the case
where the two numbers are equal - in this case, we want an identity
function.
I was tempted to implement logarithmic mean as
Lm=: (- % -&^.)^:~:
But this has a problem with rank:
2 Lm 2
2
2 3 Lm 3 2
2.4663 2.4663
2.4663 2.4663
I could solve this with ("0) but that strikes me as inefficient.
L2=: (- % -&^.)^:~:"0
So, instead:
L=: (]*=) + - % -&^.
((L-:L2) |.) i.1e5
1
Is that worth it?
timespacex '(L |.) i.1e5'
0.0365999 5.24506e6
timespacex '(L2 |.) i.1e5'
0.0828581 3.14982e6
Probably...
A caution, though:
0 L 0
|NaN error: L
Because:
^. 0
__
So maybe the explicit rank implementation isn't such a bad idea after all?
Thanks,
--
Raul
----------------------------------------------------------------------
For information about J forums see http://www.jsoftware.com/forums.htm
