•edge — Edge modes

n•edge p gives the position on an axis of n items that each position in p reads, under the fill mode. •edge mode gives the function for another mode, "clamp", "wrap", "reflect" or "symmetric", which takes n and p the same way. •edge maps over a list of mode names, as •element maps over tags. Like an element function, a mode function displays as the call that made it, such as •edge"clamp". Positions inside the axis stay as they are in every mode.

p←¯2+⍳8ₓ
[clamp wrap reflect symmetric]←•edge "clamp" "wrap" "reflect" "symmetric"
4•edge p         ⍝ $n $n 0 1 2 3 $n $n
4 clamp p        ⍝ [0 0 0 1 2 3 3 3]ₓ
4 wrap p         ⍝ [2 3 0 1 2 3 0 1]ₓ
4 reflect p      ⍝ [2 1 0 1 2 3 2 1]ₓ
4 symmetric p    ⍝ [1 0 0 1 2 3 3 2]ₓ

Fill gives 64-bit floats whatever the float pref, with NaN for a position outside the axis. The other modes give exact integers. "reflect" leaves out the edge item, as NumPy’s and PyTorch’s reflect do. "symmetric" repeats it, as NumPy’s symmetric does. An axis of length 0 gives NaN in every mode. A NaN in p stays NaN.

A selection reads the positions that •edge gives. A NaN position reads the fill, and a write through it writes nothing. A position with spaces in it goes in parentheses inside brackets:

x←10 20 30 40 ⋄ i←⍳4ₓ ⋄ clamp←•edge "clamp"
x.[(4•edge i-1)]     ⍝ 0 10 20 30
x.[(4 clamp i-1)]    ⍝ 10 10 20 30

Each mode is arithmetic on positions. Wrap is n|p, and clamp is 0⌈(n-1)⌊p. A bare negative position counts back from the end, as in every selection.

Windows and Stencil take a mode’s name as the edge of an options record, and read their windows’ positions past the ends by it, as in ["size":3 "edge":"wrap"]↕v.

Errors: DOMAIN for a mode name that isn’t one of the five, a length that isn’t a nonnegative whole number, or a position that isn’t whole.

Dot and ⌷ select.