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Computing with lots of values at once

One of the things you might have noticed is that when R prints out an answer, it puts [1] first. Like this:

> 5^2
[1] 25

What's this?

It turns out that R really works with whole vectors of values at once. The values above were just treated as 'vectors' of length one.

Note

A 'vector' is R's name for an array of values, all of the same type.

So that [1] is just there to tell you we are on the first value in the result, which in this case only has one entry.

Making ranges of values​

You can see this, for example, by creating a longer vector - say all the numbers from 1 to 100:

% 1:100

You should see something like:

  [1]   1   2   3   4   5   6   7   8   9  10  11  12  13  14  15  16  17  18
 [19]  19  20  21  22  23  24  25  26  27  28  29  30  31  32  33  34  35  36
 [37]  37  38  39  40  41  42  43  44  45  46  47  48  49  50  51  52  53  54
 [55]  55  56  57  58  59  60  61  62  63  64  65  66  67  68  69  70  71  72
 [73]  73  74  75  76  77  78  79  80  81  82  83  84  85  86  87  88  89  90
 [91]  91  92  93  94  95  96  97  98  99 100

Now you can see what the numbers in brackets are for - they are a visual guide to the vector of output values.
For example in the above I can see that the 1st, 19th, 37th, ... and 91st values are at the start of the rows.

Note

The syntax 1:100 is shorthand for 'list all the numbers from a to b'. Another way to write this is using the seq() function:

seq( from = 1, to = 100 )

Feel free to try some different ranges of numbers here. You can also try the by argument to count in steps:

seq( from = 1, to = 100, by = 5 )

Make sure you know what this does.

Concatenating values​

Another good way to create vectors is to use the c() (shorthand for 'concatenate') function. It sticks together its arguments into a longer vector:

> c( "This", "is", "a", "vector", "of", "strings )
[1] "This"    "is"      "a"       "vector"  "of"      "strings"
Question

What do you think this will produce?

> c( 1:5, 11:15, 21:25 )

(Try it and see.)

Computing with vectors​

Because everything is treated as a 'vector' of values, you can easily combine this to carry out complicated arithmetic operations. For example, let's work out the first fifteen powers of 5:

> 5^(1:15)
 [1]           5          25         125         625        3125       15625
 [7]       78125      390625     1953125     9765625    48828125   244140625
[13]  1220703125  6103515625 30517578125
Note

Here the brackets around (5:15) were needed. What happens if you do just 5^1:15 instead? Why?

In general round brackets act to group an expression together, so it gets treated all as one.