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Scan (f\)

Syntax

f\ Y

f is a dyadic scalar function. Y is the argument array.

Description

Like reduce, but keeps all intermediate results. Element i of the result is f/ applied to the first i+1 elements. The result has the same shape as the input.

Scan is left-to-right: for +\ a b c d, the result is a, a+b, (a+b)+c, ((a+b)+c)+d.

Examples

      +\ 1 2 3 4 5
1 3 6 10 15
      ×\ 1 2 3 4 5
1 2 6 24 120
      ⌈\ 3 1 4 1 5
3 3 4 4 5

Higher-rank arrays

On matrices, scan works along the last axis. The result has the same shape as the input.

      +\ 3 3⍴⍳9
1 3  6
4 9 15
7 16 27

Empty arrays

Scanning an empty array returns an empty array.

See also