column and row join a second box data

Question

I want to column join

┌─┬─┬─┐
│1│1│2│
│2│4│4│
│3│9│6│
└─┴─┴─┘

and I'd like to put a=.1 2 3 as the fourth row, and then put b=.1 1 1 1 as the first column to the new boxed data. How can I do this easily? Do I have to ravel the whole thing and compute the dimention on my own in order to box it again?

Also, if I want the data i.8 to be 2 rows, do I have to calculate the other dimension 4(=8/2) in order to form a matrix 2 4$i.8? And then box it ;/2 4$i.8? Can I just specify one dimension, either the number of row or columns and ask automatic boxing or forming the matrix?

Answer 1

The answer to your question will involve learning about &. , the 'Under' conjunction, which is tremendously useful in J.

   m
┌─┬─┬─┐
│1│1│2│
│2│2│4│
│3│9│6│
└─┴─┴─┘
   a=. 1 2 3
   b=. 1 1 1 1

So we want to add each item of a to each boxed column of m . It would be perfect if we could unbox the column using unbox(>), append the item of a to the column using append (,) and then rebox the column using box (<). This undo, act, redo cycle is exactly what Under (&.) does. It undoes both its right and left arguments ( m and a ) using the verb to its right, then applies the verb to its left, then uses the reverse of the verb to its right on the result. In practice,

   m , &. > a
┌─┬─┬─┐
│1│1│2│
│2│2│4│
│3│9│6│
│1│2│3│
└─┴─┴─┘

The fact that a is unboxed when it was never boxed to begin with means that it is not changed, while m is unboxed before (,) is applied to each a . In fact this is used so often in J that &. > is assigned the name 'each'.

   m , each a
┌─┬─┬─┐
│1│1│2│
│2│2│4│
│3│9│6│
│1│2│3│
└─┴─┴─┘

Prepending a boxed version of b requires first giving it an extra dimension with laminate (,:) then transposing (|:) b and finally boxing (<) the result. The step of adding the extra dimension is required because transposing swaps the indices and b start as a one-dimensional list.

  (<@|:@,:b) 
┌─┐
│1│
│1│
│1│
│1│
└─┘ 

The rest is easy as we just use append (,) to join the boxed b with (m, each a)

  (<@|:@,: b) , m , each a
┌─┬─┬─┬─┐
│1│1│1│2│
│1│2│2│4│
│1│3│9│6│
│1│1│2│3│
└─┴─┴─┴─┘

Brackets around (<@|:@,: b) are necessary to force the correct order of execution.

For the second question, you can use i. n m to create a n X m array, which may help.

   i. 4 2
0 1
2 3
4 5
6 7
   i. 2 4
0 1 2 3
4 5 6 7

but perhaps I am misunderstanding your intentions here.

Hope this helps, bob

Answer 2

append a (with rank): ,"x a

You can simply append (,) a to your unboxed (>) input but you have to be careful with the append rank. You want to append each "item" of a, so you have right rank of "0". You want to apend to a 2-cell so you have a left rank of "2". Therefore, the , you need has rank "2 0. After the append, you rebox your data to a 2-cell with <"2.

<"2(>in)(,"2 0) a
┌─┬─┬─┐
│1│1│2│
│2│4│4│
│3│9│6│
│1│2│3│
└─┴─┴─┘

prepend b: b,

If your b has the right shape you prepend it with b,. The shape you seem to use is (boxed) 4 1:

b =: < 4 1$ 1
┌─┐
│1│
│1│
│1│
│1│
└─┘
b,in
┌─┬─┬─┬─┐
│1│1│1│2│
│1│2│4│4│
│1│3│9│6│
│1│1│2│3│
└─┴─┴─┴─┘