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 word of warning.

Look what happens when we try to create the new temperature matrix from the already existing temperature vectors

      TEMPERATURE_DATA1 ← 21.4 'Day 1, 07:42' 21.8 'Day 1, 08:47'
      TEMPERATURE_DATA2 ← 22.8 'Day 1, 18:23' 21.5 'Day 1, 19:30'
      TEMPERATURE_ARRAY ← 2 2 2 ⍴ TEMPERATURE_DATA1 TEMPERATURE_DATA2

      TEMPERATURE_ARRAY
 21.4  Day 1, 07:42  21.8  Day 1, 08:47   22.8  Day 1, 18:23  21.5  Day 1, 19:30  
 21.4  Day 1, 07:42  21.8  Day 1, 08:47   22.8  Day 1, 18:23  21.5  Day 1, 19:30  

 21.4  Day 1, 07:42  21.8  Day 1, 08:47   22.8  Day 1, 18:23  21.5  Day 1, 19:30  
 21.4  Day 1, 07:42  21.8  Day 1, 08:47   22.8  Day 1, 18:23  21.5  Day 1, 19:30  

Compared to the expected result, which is

21.4 Day 1, 07:42
21.8 Day 1, 08:47

22.8 Day 1, 18:23
21.5 Day 1, 19:30

Replacing the vectors by strings, the situation is a little more clear

      ARRAY ← 2 2 2 ⍴ 'TEMPERATURE_DATA1' 'TEMPERATURE_DATA2'
      ARRAY
 TEMPERATURE_DATA1  TEMPERATURE_DATA2 
 TEMPERATURE_DATA1  TEMPERATURE_DATA2 

 TEMPERATURE_DATA1  TEMPERATURE_DATA2 
 TEMPERATURE_DATA1  TEMPERATURE_DATA2 

In APL, elements of arrays can be of any rank. In the above code, we've accidentally created an array of vectors rather than an array of their scalars! This is because we did not combine the vectors into a larger vector, but made a new vector whose elements are TEMPERATURE_DATA1 and TEMPERATURE_DATA2.

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

      TEMPERATURE_DATA1 ← 21.4 'Day 1, 07:42' 21.8 'Day 1, 08:47'
      TEMPERATURE_DATA2 ← 22.8 'Day 1, 18:23' 21.5 'Day 1, 19:30'
      TEMPERATURE_ARRAY ← 2 2 2 ⍴ TEMPERATURE_DATA1 , TEMPERATURE_DATA2
21.4 Day 1, 07:42
21.8 Day 1, 08:47

22.8 Day 1, 18:23
21.5 Day 1, 19:30

Boxing

The ]Box user command controls how array output is displayed, with levels of nesting shown as boxes.

      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││     ││
│     ││└─────┴───┘│     ││
│     │└───────────┴─────┘│
└─────┴───────────────────┘