Kip asked:
> Is there a tacit way?
> mp =: +/ . * NB. matrix product
> mpwr =: 4 : 'x mp^:y =i.#x' NB. square matrix x to integer power y
> A =: 1 1 ,: 1 0
The gerund form of ^: allows you to write such expressions tacitly. The
full form is x f^:(newX`thePower`newY) y which resolves to (x newX y) f^:(x
thePower y) (x newY y), or, effectively, newX f^:thePower newY . In your
case:
mpwrT=:mp^:([`]`(=@i.@#@[))
A mpwrT 3
3 2
2 1
A mpwrT _1
0 1
1 _1
Here, newX=:[ , i.e. the x argument to the derived function is just a
pass-through of the original x, which is common enough that ^: provides a
shortcut:
x f^:(thePower`newY) y is equivalent to x f^:([`thePower`newY) y . So you
could simplify this to:
mpwrT =: mp^:(]`(=@i.@#@[))
-Dan
PS: A really subtle implication of the gerund form of ^: is that it lets you
do sneaky things write code that uses simple-looking powers (e.g. f^:]) but
then _pass in a pre-calculated gerund as an argument_.
For example, here's a series of equivalent, but increasingly indirect, ways
to express the largest 32-bit signed integer:
(2^31)-1
(2^(32-1))-1
(2^((2^5)-1))-1
_1+2^ _1+2^ 5
(_1+2&^)(_1+2&^) 5
(_1+2&^)^:2: 5
2&(_1+^)^:2: 5
2 (_1+^)^:2: 5
2 <:@^^:2: 5
2 <:@^^:(2:`5:) ''
<:@^^:(2:`2:`5:)~ ''
<:@^^:]~ 2:`2:`5:
This last separates the core function, exponentiate-and-decrement, and the
underlying data, 2 2 5. It's the moral equivalent of <:@^/ 2 2 5 , but at
the meta-function level. For more fun with this, see
[1] Calculating 2147483647:
http://www.jsoftware.com/jwiki/Puzzles/2147483647
[2] Using our ^: for good
http://www.jsoftware.com/pipermail/programming/2012-February/027116.html
[3] But ^: corrupts
http://www.jsoftware.com/pipermail/programming/2013-January/031234.html
[3] ... absolutely:
http://www.jsoftware.com/pipermail/programming/2013-January/031236.html
Mwahahahahaa.
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