... and my last remark probably deals more with efficiency than
effectiveness -- I sometimes fight for words even in my mother tongue.
-M
At 2016-08-31 06:33, you wrote:
Don -
That's been exacly the idea behind what I called "gm1" (taking the
roots first) ...
The Log approach "gm2" however proves to be a little bit more effective:
10000 timespacex 'gm1 >: ? 6 $~ 2^10'
0.000185607 50816
10000 timespacex 'gm2 >: ? 6 $~ 2^10'
0.000110259 42752
-M
At 2016-08-31 03:24, you wrote:
How about this-it fits the definition of "nth root of product of n items"
gmean =: # %: */
(gmean,gm1)>: ? 6 $~ 637
2.98625 2.98625
(gm0,gm1,gm2,gmean)>:?6$~637
2.97123 2.97123 2.97123 2.97123
(gm0,gm1,gm2,gmean) >:?6$~637
_ 3.04854 3.04854 _
(gmean, gm1)s=:>:?6$~638
_ 3.06565
b=: 638 %: s
*/b
3.06565
(amean s) ^ 638
*/s
The problem appears when */ results in an overflow and is detected
as infinite
*/ 638#3
2.5314e304
*/ 638#4
638 %:638#4
1.00218 1.00218 1.00218 1.00218218 1.00218 1.00218 ...
*/ 638 %:638#4
The advantage lies with taking the roots first for numbers >1
Don Kelly
On 8/26/2016 4:38 AM, Martin Kreuzer wrote:
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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