Vectors

This part will cover

• Creating vectors
• Spaces Separate Scalars

---

You are an astronaut aboard the International Space Station. You are currently orbiting the Earth at an altitude of 413km at a speed of 28,013km/h.

In brief intervals of time spent waiting between tasks, you enjoy logging temperatures from sensors all around the ship into a small notebook. Unfortunately for you, your notebook’s completely filled, and none of your colleagues seem to share your enthusiasm for data collection. Unfortunately for mission control, you’ve decided to use critical APL machines on board to store your data.

Typing as fast as possible without the aid of gravity, you manage to write some data without being caught.

      TEMPERATURE_PAGE1_YEAR1_DAY2_HOUR7_MINUTE42 ← 21.4
      TEMPERATURE_PAGE1_YEAR1_DAY2_HOUR8_MINUTE47 ← 21.8
      TEMPERATURE_PAGE1_YEAR1_DAY2_HOUR10_MINUTE10 ← 22.0
      TEMPERATURE_PAGE1_YEAR1_DAY2_HOUR12_MINUTE01 ← 21.5
      TEMPERATURE_PAGE1_YEAR1_DAY2_HOUR14_MINUTE36 ← 21.3
      TEMPERATURE_PAGE1_YEAR1_DAY2_HOUR16_MINUTE50 ← 22.3
      TEMPERATURE_PAGE2_YEAR1_DAY2_HOUR18_MINUTE23 ← 22.8
      TEMPERATURE_PAGE2_YEAR1_DAY2_HOUR19_MINUTE30 ← 21.5
      TEMPERATURE_PAGE2_YEAR1_DAY2_HOUR21_MINUTE12 ← 22.1
      TEMPERATURE_PAGE2_YEAR1_DAY3_HOUR7_MINUTE15 ← 22.0
      TEMPERATURE_PAGE2_YEAR1_DAY3_HOUR8_MINUTE30 ← 21.9
      TEMPERATURE_PAGE2_YEAR1_DAY3_HOUR9_MINUTE45 ← 22.4

This is not the most efficient, or readable, method to input data into your system, and while flicking through your APL notes now crowded with temperatures, you refresh your workspace and instead decide to store your data using vectors.

---

Vectors are lines of values. They are defined by writing values separated by one or more spaces.

The order of elements in a vector matters! Each element is given a number called an index according to the order in which they were written. Indices can be used to access the elements of a vector, they start at 1 and increase by one for each new element.

To show the difference between vectors and scalars, we give some examples of both.

      ⍝ Scalars
      SUM ← ¯1÷12
      EPSILON ← 2*¯53
      PIGS ← 3
      BROTHERS ← 7
      ⍝ Note that the decimal separator in APL is the dot
      PI ← 11.001001
      THIEVES ← 40
      PRIME ← 57
      MAGIC ← 1597463007

      ⍝ Vectors
      FIBB ← 1 1 2 3 5 8 13 21 34 55 89 144 233 377 610 987 1597 2584 4181
      QUARTER ← 1 ¯2 3 ¯4 5 ¯6 7 ¯8 9 ¯10 11 ¯12 13 ¯14 15 ¯16 17 ¯18
      KEY ← 9 249 17 2 157 116 227 91 216 65 86 197 99 86 136 192 

Scalar variables can be used to construct new vectors, such as in the following

      LIST ← SUM EPSILON PIGS BROTHERS PI THIEVES PRIME MAGIC
      LIST
¯0.08333333333 1.110223025E¯16 3 7 11.001001 40 57 1597463007

Selecting indices from a vector can be done using square brackets as shown below

      ⍝ Selecting a single element using an index
      LIST[1] 
¯0.08333333333

      ⍝ Selecting multiple values using indices
      LIST[3 4 5]
3 7 11.001001

      ⍝ Selecting multiple values using a vector of indices
      INDICES ← 5 6 7
      LIST[INDICES] 
11.001001 40 57

Finally, returning to our original problem, we can represent the lists of temperatures as vectors

      TEMPERATURE_PAGE1 ← 21.4 21.8 22.0 21.5 21.3 22.3
      TEMPERATURE_PAGE2 ← 22.8 21.5 22.1 22.0 21.9 22.4

      TEMPERATURE_PAGE1[1 2 3]
      21.4 21.8 22.0