Skip to content

Nested arrays

This part will cover

  • Basics of nested arrays
  • How to catenate vectors properly

Be warned, elements of arrays can be vectors, or matrices, or arrays of higher rank in their own right! We will discuss this in depth in Chapter 5, so take this section as a warning.

Recall that in previous sections our temperature arrays contained both numbers and vectors of characters.

      T1
┌────┬───────────┐
│21.4│Day 1 07:42│
├────┼───────────┤
│21.8│Day 1 08:47│
├────┼───────────┤
│22  │Day 1 10:10│
├────┼───────────┤
│21.5│Day 1 12:01│
├────┼───────────┤
│21.3│Day 1 14:36│
├────┼───────────┤
│22.3│Day 1 16:50│
└────┴───────────┘

Because the contents of this array are mixed, if boxing is enabled, APL draws boxes to separate the entries visually.

This also means that it's possible to accidentally create a matrix of vectors rather than a matrix of their elements. Suppose we created the full array TData immediately from T1 and T2 like so

      T1 ← [ 21.4 'Day 1 07:42' ⋄ 
            21.8 'Day 1 08:47' ⋄
            22.0 'Day 1 10:10' ⋄
            21.5 'Day 1 12:01' ⋄
            21.3 'Day 1 14:36' ⋄
            22.3 'Day 1 16:50' ]

      T2 ← [ 22.8 'Day 1 18:23'  ⋄ 
             21.5 'Day 1 19:30'  ⋄
             22.1 'Day 2, 21:12' ⋄
             22.0 'Day 3, 07:15' ⋄
             21.9 'Day 3, 08:30' ⋄
             22.4 'Day 3, 09:45' ]

      TData ← 2 2 6 ⍴ T1 T2

We would get a very large array of the vectors T1 and T2! (Try it!)

In APL, elements of arrays can be of any rank. In the above code, we create an array of vectors rather than an array of their scalars because T1 T2 is a vector whose elements are T1 and T2.

The proper way to combine two vectors into a single longer vector is using the catenate , function, generally joining two arrays along a common edge. Monadically, the ravel , function can be used to "unravel" a matrix into a vector of its elements in top-down left-right order, called ravel order.

      WORD ← 3 2 2 ⍴ 'BOROSILICATE'
      WORD
BO
RO

SI
LI

CA
TE

      ,WORD
BOROSILICATE

      WORD,'T'
BOT
ROT

SIT
LIT

CAT
TET

      WORD,WORD
BOBO
RORO

SISI
LILI

CACA
TETE

      T1 ← [ 21.4 'Day 1 07:42' ⋄ 
            21.8 'Day 1 08:47' ⋄
            22.0 'Day 1 10:10' ⋄
            21.5 'Day 1 12:01' ⋄
            21.3 'Day 1 14:36' ⋄
            22.3 'Day 1 16:50' ]

      T2 ← [ 22.8 'Day 1 18:23'  ⋄ 
             21.5 'Day 1 19:30'  ⋄
             22.1 'Day 2, 21:12' ⋄
             22.0 'Day 3, 07:15' ⋄
             21.9 'Day 3, 08:30' ⋄
             22.4 'Day 3, 09:45' ]

      TData ← 2 2 6 ⍴ T1,T2
      TData
┌────┬───────────┐
│21.4│Day 1 07:42│
├────┼───────────┤
│21.8│Day 1 08:47│
├────┼───────────┤
│22  │Day 1 10:10│
├────┼───────────┤
│21.5│Day 1 12:01│
├────┼───────────┤
│21.3│Day 1 14:36│
├────┼───────────┤
│22.3│Day 1 16:50│
└────┴───────────┘
┌────┬───────────┐
│22.8│Day 1 18:23│
├────┼───────────┤
│21.5│Day 1 19:30│
├────┼───────────┤
│22.1│Day 2 21:12│
├────┼───────────┤
│22  │Day 3 07:15│
├────┼───────────┤
│21.9│Day 3 08:30│
├────┼───────────┤
│22.4│Day 3 09:45│
└────┴───────────┘

Boxing

In TryAPL, boxing is enabled by default; however, to manually control boxing, the ]Box user command can be used.

      nested ← 2 2 ⍴ (⍳3) ('  ') ('   ') (2 2 ⍴ ('  ') (⍳3) (2 2 ⍴ (⍳3) ('  ') ('   ') (⍳2)) ('   '))
      nested
1 2 3                        
                1 2 3  
   1 2 3               
          1 2          

      ]Box on
Was OFF
      nested
┌─────┬───────────────────┐
│1 2 3│                   │
├─────┼───────────────────┤
│     │┌───────────┬─────┐│
│     ││           │1 2 3││
│     │├───────────┼─────┤│
│     ││┌─────┬───┐│     ││
│     │││1 2 3│   ││     ││
│     ││├─────┼───┤│     ││
│     │││     │1 2││     ││
│     ││└─────┴───┘│     ││
│     │└───────────┴─────┘│
└─────┴───────────────────┘