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 as well! 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 00010101.074200 21.8 00010101.084700
       TEMPERATURE_DATA2 ← 22.8 00010101.182300 21.5 00010101.193000 
       TEMPERATURE_ARRAY ← 2 2 2 ⍴ TEMPERATURE_DATA1 TEMPERATURE_DATA2

       TEMPERATURE_ARRAY
┌───────────────────────────────┬──────────────────────────────┐
│21.4 10101.0742 21.8 10101.0847│22.8 10101.1823 21.5 10101.193│
├───────────────────────────────┼──────────────────────────────┤
│21.4 10101.0742 21.8 10101.0847│22.8 10101.1823 21.5 10101.193│
└───────────────────────────────┴──────────────────────────────┘
┌───────────────────────────────┬──────────────────────────────┐
│21.4 10101.0742 21.8 10101.0847│22.8 10101.1823 21.5 10101.193│
├───────────────────────────────┼──────────────────────────────┤
│21.4 10101.0742 21.8 10101.0847│22.8 10101.1823 21.5 10101.193│
└───────────────────────────────┴──────────────────────────────┘

compared to the expected result, which is

21.4 00010101.074200 
21.8 00010101.084700

22.8 00010101.182300 
21.5 00010101.193000

Attempting to access the elements of the rank 3 array returns vectors, this is because we’ve accidentally created an array of vectors rather than an array of their elements.

If we replace TEMPERATURE_DATA1 and TEMPERATURE_DATA2 with scalars, the situation is a bit more clear.

       ARRAY ← 2 2 2 ⍴ 'AB'
       ARRAY
A B
A B

A B
A B

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 00010101.074200 21.8 00010101.084700
       TEMPERATURE_DATA2 ← 22.8 00010101.182300 21.5 00010101.193000 
       TEMPERATURE_ARRAY ← 2 2 2 ⍴ TEMPERATURE_DATA1 , TEMPERATURE_DATA2
21.4 10101.0742
21.8 10101.0847

22.8 10101.1823
21.5 10101.193

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