Sum of each two elements using vector functions

Question

How to get sum of eath two elements with the vector functions? I want the same result as:

{x+y}':[1 2 3 2 1]

Why this approach gives something different than first one?

sum':[1 2 3 2 1]

Answer 1

sum is not the same as {x+y}.

sum has rank 1 meaning it takes one input and sums the elements of that input.

It can sum an atom:

q)sum 1
1

a uniform list

q)sum 1 2
3

or a list of lists

q)sum(1 2;3 4)
4 6

{x+y} is rank 2 meaning it requires two inputs.

q){x+y}[1;2]
3
q){x+y}[1 2;3 4]
4 6

Giving it an atom, a single list, or a list of lists leads to projections

q){x+y}1
{x+y}[1]
q){x+y}1 2
{x+y}[1 2]
q){x+y}(1 2;3 4)
{x+y}[(1 2;3 4)]

Since each-prior (':) creates binary pairs from the input and attempts to apply a rank 2 function, it works as intended on your rank 2 function {x+y}.

But since sum is not rank 2 the each-prior doesn't generate pairs in the same way, it's equivalent to doing

q){x}':[1 2 3 2 1]
1 2 3 2 1
q){sum x}':[1 2 3 2 1]
1 2 3 2 1

You could force it to be rank 2:

q){sum(x;y)}':[1 2 3 2 1]
1 3 5 5 3

but this gives a different result since sum ignores nulls while + doesn't.

q)sum(0N;1)
1
q)0N+1
0N

Finally, an alternative way to achieve this using sum (and without using each-prior) is to shift the vector using prev and then sum

q){sum(prev x;x)}[1 2 3 2 1]
0N 3 5 5 3