Roger worked it out & put it into the interpreter.
Look on his works, ye mighty, and despair.
Henry Rich
On 5/31/2013 10:00 PM, elton wang wrote:
I guess this may deserve a new thread:
for the inverse of m&|: like
3&|: b._1
(] |:~ 3 C.^:_1 i.@#@$) :.(3&|:)
How does J find this inverse? is this explicitly coded in J or J automatically
figures this out by some rules? Either way, this is amazing.
________________________________
From: Henry Rich <[email protected]>
To: [email protected]
Sent: Friday, May 31, 2013 9:26 PM
Subject: Re: [Jprogramming] zscore in J either column wise or row wise - basic
question on rank
It looks to me like that's pretty close to working, except that you
always want to apply v to rows, i. e. rank 1, i. e.
colOrRow =. 2 : ' v"1`(v"1 &.|:)@.m'
but now I must accuse you of incomplete generalization. Suppose the
operand has higher rank? Isn't what you really want to apply v along a
given axis? And, come to think of it, shouldn't we allow v to have any
rank, and apply it to selected axes? I would switch the meanings of u
and v, and write
onaxes =: 2 : 'u&.(n&|:)'
For rows, you would write
u"1 onaxes 0
for columns,
u"1 onaxes 1
You could have
onaxis =: 2 : 'u"1&.(n&|:)'
but I think that's a special case.
Wait a minute... this means you would have to have an inverse of m&|: .
What would that be? I mean, you would have to take the result, which
might have any rank, and undo the transpose... how?
2&|: b. _1
(] |:~ 2 C.^:_1 i.@#@$) :.(2&|:)
3&|: b. _1
(] |:~ 3 C.^:_1 i.@#@$) :.(3&|:)
I can't prove that that's right. But, knowing Roger, I bet it is.
Henry Rich
On 5/31/2013 8:35 PM, elton wang wrote:
thanks Henry,
to generalize the question, how do I define a conjuction colOrRow such that for
any verb v:
0 colOrRow v is to apply v along row and combine the results row wise, while 1
colOrRow v is to apply v along column and combine the results column wise?
I tried colOrRow =. 2 : ' v`(v"1 &.|:)@.m'. but this is not working.
________________________________
From: Henry Rich <[email protected]>
To: [email protected]
Sent: Friday, May 31, 2013 8:16 PM
Subject: Re: [Jprogramming] zscore in J either column wise or row wise - basic
question on rank
A good testcase for the new dissect tool!
load '~addons/debug/dissect/dissect.ijs'
z0 =. (- mean) % stddev
z0 i. 3 4
|length error: z0
| z0 i.3 4
what's it doing in there?
z0 f.
(- (+/ % #)) % %:@(+/@:*:@(-"_1 _ (+/ % #)) % <:@#)
run dissect on that:
ds '((- (+/ % #)) % %:@(+/@:*:@(-"_1 _ (+/ % #)) % <:@#)) i. 3 4'
the display shows that there is agreement error in (- mean). Oh yeah,
to work at high rank, you have to put the correct rank on - and % :
z0 =. (-"_1 _ mean) %"_1 _ stddev
z0 i. 3 4
_1 _1 _1 _1
0 0 0 0
1 1 1 1
z0"1 i. 3 4
_1.1619 _0.387298 0.387298 1.1619
_1.1619 _0.387298 0.387298 1.1619
_1.1619 _0.387298 0.387298 1.1619
I don't know if that's correct, but the ranks are right.
Henry Rich
On 5/31/2013 7:57 PM, elton wang wrote:
if I define zscore as z0 =. (- mean) % stddev, z0 works for rank 1 array.
For a rank 2 array like a=. i. 3 4, if I want to get zscore along either column
or row, I could define
z1 =. [: |: stddev %~ |: - mean
z1 i. 3 3
_1 _1 _1
0 0 0
1 1 1
and
z1"1 i. 3 3
_1 0 1
_1 0 1
_1 0 1
My question is that z1 uses |: twice and looks awkward. If there any clever way
to implement z1 by rank annotation or something?
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