Terrence Brannon wrote:
>However, I think there should be a period between "x" and "If"
Good catch.
>Also, I find this description confusing. What does it mean to index an
>array? Are y and x both arrays?
In J, all data (AKA nouns AKA variables) are arrays. Even a simple scalar like
5 is an array. So, yes, both x and y are arrays.
An index is a way to refer to a part of an array without regard to the actual
value in that array. In lots of languages, you say something like
array[index] . In J, you say index { array .
If you think about it, pulling parts out of an array is an action like any
other. An action is a verb. The authors of J realized this, and so, instead
of giving indexing special syntax as in other languages, they made it a normal
verb (function).
At first, coming from other languages, this is frustrating and annoying. For
example, you can no longer say:
array[14] = 52; // J equivalent is array =: 52 ( 14} ) array
But you soon learn how powerful and useful this model is. You can calculate
indicies (even multi dimensional), pull them out of the array, put them back,
ALL WITHOUT REFERENCE TO THE SPECIFIC ARRAY. It allows one to abstract a level
from the array; all arrays of the same shape are, in this sense, identical;
indistinguishable.
A simple example: pulling out the very middle atom of an array. J makes this
easy:
center =: {~ [: <@:(<"0) (#: <.@:-:@:(*/))@:$ NB. Examples in PS
which will work correctly on all arrays -- of any rank, shape, or type.
It's either impossible or very awkward to reproduce this example in many other
languages. Often, you need other syntax (i.e. compiled source code) to
reference a multidimensional array (e.g. array[3;14] or array[3][14] ).
This limitation means you must (at least) know an array's rank in advance.
> Is there some tagging ... such that J knows the array
> is a permutation and not just an array?
No, a permutation is simply any ordering of the integers i.N (where N is
the length of the array you're indexing and is known as the "order" of the
permutation). So the following are all permutations:
0 1 2 3
3 2 1 0
2 0 1 3
5 4 1 2 0 3
1 0
0
0#0 NB. No indicies at all
etc. There are many ways of generating permutations. The verbs /: and \:
produce special permutations which tell you how to sort an array. So (/:x) {
x will sort x (doesn't matter what x is; can be any type, rank, or shape).
Take a look at the verbs A. and C. too.
Hope this helps,
-Dan
PS:
center 1 2 3 4 5
3
center 'ABC|DEF'
|
center 0
0
center 1 2 3 , 4 5 6 ,: 7 8 9
5
center i. 5 6 8 3 2 4
2880
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