Hi all -
Sharing something I observed ...
While the definitions (for arithmetic and geometric mean)
amean=: +/ % #
and
gmean=: */ %:~ #
are nice to look at as a pair (because of symmetry) I prefer this
definition of geometric mean
gmean=: [: */ # %: ]
or
NB. using the Log domain
gmean=: [: ^ [: amean ^.
because, given these (intermediate) definitions
NB. often found
gm0=. */ %:~ #
NB. taking the roots first, then multiply
gm1=. [: */ # %: ]
NB. definition found on (&.:) page of NuVoc
gm2=. amean &.: ^.
I got these results (see gm0 failing while the other two hold)
(gm0,gm1,gm2) >: ? 6 $~ 637
3.04409 3.04409 3.04409
(gm0,gm1,gm2) >: ? 6 $~ 638
_ 3.05264 3.05264
(gm0,gm1,gm2) >: ? 6 $~ 2^24
_ 2.99357 2.99357
under J v8.04 on a 32-bit Vista machine.
Thanks
-M
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