The Index Function `⍳`

DEVELOPERS NOTE

For the moment ⍳ is returning an unindexed array - this might need to change.

Monadic Use On Integers Scalars

⍳ is a monadic function which when applied to a vector of integers or a scalar generates a matrix of indices.

⍳ 2

1 2

Monadic Use On Boolean Scalars

A boolean scalar will be cast to an integer scalar

⍳ 1

Monadic Use On Integers Vectors

It is multidimensional, of course:

⍳3 2 1

┌─────┐
│1 1 1│
└─────┘
┌─────┐
│1 2 1│
└─────┘

┌─────┐
│2 1 1│
└─────┘
┌─────┐
│2 2 1│
└─────┘

┌─────┐
│3 1 1│
└─────┘
┌─────┐
│3 2 1│
└─────┘

⍳ on a vector of one might surprise you

A ← 1 ⍴ 4
⍳ A

results in:

┌─┐ ┌─┐ ┌─┐ ┌─┐
│1│ │2│ │3│ │4│
└─┘ └─┘ └─┘ └─┘

Use With Other Data Types

If applied to a boolean scalar ⍳ will return a degenerate multidimensional scalar of type array with a null argument if any of the elements are set to zero.

⍳ 1 1 1 0

  ____
 |  _ \
 | |_) | _____      ____ _ _ __ ___
 |  _ < / _ \ \ /\ / / _` | '__/ _ \
 | |_) |  __/\ V  V / (_| | | |  __/
 |____/ \___| \_/\_/ \__,_|_|  \___|

If you try and print out a structure contrainig a degenerate multidimensional scalar of type array it will blow up. See the Stdlib Print Trees Function documentation.

It is degenerate because it keeps its dimensionality (but the presence of a single 0 causes it to collapse:

A ← ⍳ 1 1 1 0
⍴ A

1 1 1 0

However if all the elements are 1 it will return a degenerate multidimensional array of type array with the value 1

⍳ 1 1 1 1

┌───────┐
│1 1 1 1│
└───────┘

Attemps to use ⍳ on a vector of other values will throw a DOMAIN ERROR:

⍳ 3 2 1.1

giving:

Error
⍳ 3 2 1.1
--^
DOMAIN ERROR [⍳ only accepts integer arguments and was called with: [3,2,1.1] ] on line 1 at character 3

Attempts to use ⍳ on a scalar float will also throw an error (even if the float evaluates to an integer):

⍳ 1.0