`42 * 2`

`84`

You’ve already seen how to assign variables in Julia, which is not so dissimilar from `R`

. Many other things will be familiar as well, and throughout these tutorials, we will try to point out where differences exist or may be confusing.

Let’s start with Numbers!

Julia was designed for technical and mathematical computing, and a great deal of effort has been put in to make math in code look like and work like math written on paper.

This means that a lot of simple operations work just like you would expect:

`42 * 2`

`84`

`1.3e4 / 1000`

`13.0`

`5 % 2 # remainder`

`1`

Note

`#`

makes the remainder of the line into a comment, just like R and Python

```
# order of operations is PEMDAS
1 + 2)^3 * 2 + 1 # 3^3 * 2 + 1 => 27 * 2 + 1 => 54 + 1 (
```

`55`

Some mathematical operations use **functions**, which just like in R, are called using the function name, with arguments to the function surrounded by parentheses:

`sqrt(10)`

`3.1622776601683795`

In R, the above looks like:

```
> sqrt(10)
1] 3.162278 [
```

But many functions of this sort also have unicode-based equivalents. For example, the following is identical to `sqrt(10)`

:

`10 # this is typed \sqrt<TAB> √`

`3.1622776601683795`

Note

In fact, all of the mathematical symbols above are actually Julia functions. For example, `3 + 4`

is actually just shorthand for `+(3, 4)`

You’ll learn much more about Julia functions in a future tutorial.

Boolean values are lowercase in Julia (eg `true`

and `false`

rather than `TRUE`

and `FALSE`

), but you can do basic comparisons as you do in R:

`1 < 3 # 1 is less than 3`

`true`

`5 * 2 == 11 # 5 * 2 is equal to 11`

`false`

And you can negate a boolean expression with `!`

`5 * 2 == 11) # or, in this case, 5 * 2 != 11 !(`

`true`

There are also many functions that return boolean values that are often used for **conditional evaluation** (if / else statements).

`isodd(3)`

`true`

`isodd(3) # read "3 is not odd" !`

`false`

Boolean expressions can also be combined using `&&`

for “AND” and `||`

for “OR”. `&&`

returns `true`

if both statements are `true`

, while `||`

returns `true`

if either statement is `true`

.

For example:

`isodd(3) && isodd(4) # 3 is odd AND 4 is odd`

`false`

`iseven(3) || iseven(4) # 3 is even OR 4 is even`

`true`

Caution

In Julia Boolean values are a subtype of `Integer`

, and can be used in some mathematical operations as 0 (for `false`

) and 1 (for `true`

). For example:

```
julia> 1 + true
2
```

But the reverse is not true. That is, you cannot use `1`

in an if/else statement. This is in contrast to R, where any number other than `0`

is considered `TRUE`

, and `0`

is considered `FALSE`

.

```
$> ifelse(1, 10, 20)
r1] 10
[
$> ifelse(2, 10, 20)
r1] 10
[
$> ifelse(0, 10, 20)
r1] 20 [
```

In Julia, this will throw an error:

```
julia> ifelse(1, 10, 20)
ERROR: TypeError: non-boolean (Int64) used in boolean context
```

You can, however, explicitly convert a Boolean to an integer with eg `Int(false)`

and `Int(true)`

, or convert a 1 or 0 to `true`

or `false`

with eg `Bool(1)`

.

Using Boolean expressions is quite common in data analysis, for example to filter on observations that meet some criteria. We will see many more examples in future tutorials.

In Julia, strings are surrounded by double quotes (`"`

) only. Single quotes are only used for individual characters

`'C'`

`'C': ASCII/Unicode U+0043 (category Lu: Letter, uppercase)`

```
# this is an error
'Hello, World!'
```

`ErrorException: ErrorException("syntax: character literal contains multiple characters")`

```
# this is what we meant
"Hello, World!"
```

`"Hello, World!"`

To concatenate strings, use the `string()`

function, or **multiply** them.

`string("Hello", " ", "world!")`

`"Hello world!"`

`"Hello" * " " * "world!"`

`"Hello world!"`

Pattern matching can be done with the `contains()`

function. This is a boolean function that takes 2 arguments: the first is a string that you’re searching in, the second is that pattern that you’re searching for.

`contains("banana", "ana")`

`true`

`contains("banana", "lana")`

`false`

If you know regular expressions, you can use those as the second argument as well. In Julia, you can make a regular expression using a special “string literal” macro, eg `r"my regex"`

.

Don’t worry if you don’t know what this means.

`contains("banana", r"(an){2}")`

`true`

There are also a handful of functions for modifying strings.

`= "Let's see what I can do with this 😀" my_string `

`"Let's see what I can do with this 😀"`

`uppercase(my_string)`

`"LET'S SEE WHAT I CAN DO WITH THIS 😀"`

`lowercase(my_string)`

`"let's see what i can do with this 😀"`

`replace(my_string, "this" => "that")`

`"Let's see what I can do with that 😀"`

`split(my_string, 'w') # this makes a "vector" of substrings`

```
3-element Vector{SubString{String}}:
"Let's see "
"hat I can do "
"ith this 😀"
```

For (MUCH) more on strings, check out the strings tutorial.

Things like strings, integers, and floating point values are examples of “scalar” types, but you’re probably also familiar with container types, such as vectors, which are 1-dimensional, ordered containers.

In R, vectors are created with the syntax `c(10,20,30)`

. In Julia, the same operation is `[10,20,30]`

.

As in R, vectors can be “indexed” or “sliced” using brackets. For example, in R

```
> my_vec <- c(10,20,30,40,50)
> my_vec[3]
1] 30
[> my_vec[3:5]
1] 30 40 50
[> my_vec[c(1,4)]
1] 10 40 [
```

In Julia, the same tasks are accomplished thusly:

`= [10, 20, 30, 40, 50] my_vec `

```
5-element Vector{Int64}:
10
20
30
40
50
```

`3] my_vec[`

`30`

`3:5] my_vec[`

```
3-element Vector{Int64}:
30
40
50
```

`1, 4]] my_vec[[`

```
2-element Vector{Int64}:
10
40
```

Julia also has a special keyword `end`

that can stand in for the last index of the container.

`end-2:end] my_vec[`

```
3-element Vector{Int64}:
30
40
50
```

Vectors in Julia are “mutable”, which means you can change the contents - updating individual indices, or adding and removing elements.

```
= [10, 20, 30, 40, 50]
new_vec 3] = 100 # Change the 3rd element to 100
new_vec[push!(new_vec, -1) # add -1 to the end
new_vec
```

```
6-element Vector{Int64}:
10
20
100
40
50
-1
```

These operations are equivalent to the following in R:

```
> my_vec[3] <- 100
> append(my_vec, -1)
1] 10 20 100 40 50 -1 [
```

Caution

There is also a function `append!()`

in Julia that acts on vectors. Unlike in R, this function is not typically used to add a single element, but rather to add each element of another collection. Note this difference in the following:

```
= [0.0, "hello", 42]
a_vector push!(a_vector, ['a', 'b'])
a_vector
```

```
4-element Vector{Any}:
0.0
"hello"
42
['a', 'b']
```

```
= [0.0, "hello", 42]
a_vector append!(a_vector, ['a', 'b'])
a_vector
```

```
5-element Vector{Any}:
0.0
"hello"
42
'a': ASCII/Unicode U+0061 (category Ll: Letter, lowercase)
'b': ASCII/Unicode U+0062 (category Ll: Letter, lowercase)
```

There are a number of other container types in Julia as well, some of which are mutable, and some of which are not. We’ll get to some examples later, but in general, they use the same indexing convention (eg `the_container[the_index]`

).

A `Matrix`

in Julia is a two-dimensional array, and works much like a `Vector`

, with the added syntax that you can index in two dimensions, separated by a `,`

where the first index refers to the row number, and the second index refers to the column number. For aficionados, Julia is “column major”.

Matrices can be constructed using the following multi-line syntax:

```
= [
my_matrix 1 10 100
2 20 200
3 30 300
4 40 400
]
```

```
4×3 Matrix{Int64}:
1 10 100
2 20 200
3 30 300
4 40 400
```

Or in a single line, replacing line breaks with `;`

:

`1 10 100; 2 20 200; 3 30 300; 4 40 400] == my_matrix [`

`true`

You can also use the `reshape()`

function to convert a vector (or other iterable) into a Matrix. The `reshape()`

function takes 3 arguments - (1) the thing being reshaped, (2) the size of the first (row) dimension, and (3) the size of the second (column) dimension.

`reshape([1, 2, 3, 4, 5, 6], 3, 2)`

```
3×2 Matrix{Int64}:
1 4
2 5
3 6
```

`1, 2] # first row, second column my_matrix[`

`10`

`2, end] # second row, last column my_matrix[`

`200`

`2:4, 1] # 2nd-4th rows, first column. Returns vector my_matrix[`

```
3-element Vector{Int64}:
2
3
4
```

`2:4, [1, 3]] # 2nd-4th rows, first and 3rd columns. my_matrix[`

```
3×2 Matrix{Int64}:
2 200
3 300
4 400
```

`2:4, [1]] # 2nd-4th rows, first column. Returns matrix my_matrix[`

```
3×1 Matrix{Int64}:
2
3
4
```

Matrices in Julia also have a linear index, which counts down the rows, column by column.

`4] my_matrix[`

`4`

`5] my_matrix[`

`10`

and you can flatten this linear index into a vector using the `vec()`

function,

`vec(my_matrix)`

```
12-element Vector{Int64}:
1
2
3
4
10
20
30
40
100
200
300
400
```

or using `reshape()`

`reshape(my_matrix, 12)`

```
12-element Vector{Int64}:
1
2
3
4
10
20
30
40
100
200
300
400
```

Note

Notice that only a single dimension is provided. If you call `reshape(my_matrix, 12, 1)`

, you would get a `Matrix`

again, only one with a single column.

Dictionaries, like “lists” in `R`

are unordered containers of `key`

, `value`

pairs. Both keys and values can have any type, eg strings, numbers (integer or float), symbols.

`= Dict("a key" => "a value", 'b' => 42, 1 => 2) my_dict `

```
Dict{Any, Any} with 3 entries:
"a key" => "a value"
'b' => 42
1 => 2
```

You access the values in a dictionary just like indexing into a vector, only you use the keys instead of linear indices.

`"a key"] my_dict[`

`"a value"`

`1] my_dict[`

`2`

If you try to index using a key that doesn’t exist, you’ll get an error, but if you’re not sure whether the key exists, you can also use the `get()`

function, which allows you to provide a value to return in case the key doesn’t exist:

`"another key"] my_dict[`

`KeyError: KeyError("another key")`

`get(my_dict, "another key", "hey, that doesn't exist!")`

`"hey, that doesn't exist!"`

Alternatively, you can check whether a dictionary has a key using the boolean `haskey()`

function (it returns either `true`

or `false`

):

`haskey(my_dict, 'a')`

`false`

`haskey(my_dict, 'b')`

`true`

Finally, you can update an entry or insert a new entry using the familiar assignment (`=`

) syntax

`"new key"] = "😉" my_dict[`

`"😉"`

It is often useful to apply the same operation on each object in a container. In R, those are often done implicitly, but in Julia, you must be explicit.

For example, let’s say we want to calculate the square root of each number in a vector. In R, you would just call `sqrt()`

on the vector:

```
$> a_vec <- c(1,2,3,4,5)
r
$> sqrt(a_vec)
r1] 1.000000 1.414214 1.732051 2.000000 2.236068 [
```

But in Julia, the square root of a vector is undefined:

`= [1, 2, 3, 4, 5] a_vec `

```
5-element Vector{Int64}:
1
2
3
4
5
```

`sqrt(a_vec)`

`MethodError: MethodError(sqrt, ([1, 2, 3, 4, 5],), 0x00000000000082cc)`

In Julia, there are several different ways to accomplish this.

Tip

In R, it’s very important to make sure all operations are vectorized, since loops written in R are incredibly slow. This is not true in Julia - loops can sometimes be faster!

`map`

The `map()`

function takes a function as its first argument, and a container as the second. It then applies the function to each item in the container, returning another container. This is analogous to the `sapply()`

function in R, though it is much more flexible as we’ll see in future tutorials.

For example:

`map(sqrt, a_vec)`

```
5-element Vector{Float64}:
1.0
1.4142135623730951
1.7320508075688772
2.0
2.23606797749979
```

Caution

Note that the order of arguments is reversed relative to `sapply()`

. In Julia, the function being applied comes first, and the container it applies to comes second.

Julia functions that are verbs can often be reasoned about if you put them into a sentence, with the arguments in the same order.

Eg. `map(sqrt, a_vec)`

is “Map `sqrt`

to `a_vec`

”, and `contains("banana", "ana")`

is “banana contains ana?”

For more on `map()`

and using it to apply functions, see the Functions tutorial.

`reduce`

, and `mapreduce`

It can also be useful to collapse a container into a single value using some operation. We can do this using the `reduce()`

function (which works similarly to `reduce()`

from the `purrr`

package in R). For example, suppose that you want to multiply all of the numbers in a vector to one another.

`reduce(*, a_vec)`

`120`

Keep in mind that you should only use *commutative* operations or operations where the order doesn’t matter. To be fast, `reduce()`

may apply the operation on items in an order you don’t expect.

The `mapreduce()`

function is like combining `map()`

and `reduce()`

. In other words, `mapreduce(op1, op2, container)`

should be identical to `reduce(op2, map(op1, container))`

, with the benefit that Julia doesn’t need to make the intermediate container (for reasons not worth going into, creating large vectors can be slow).

So, if we want to multiply all of the square roots of `a_vec`

:

`mapreduce(sqrt, *, a_vec)`

`10.954451150103324`

```
# just to prove it
reduce(*, map(sqrt, a_vec))
```

`10.954451150103324`

Containers can also be created using “comprehensions.” If you are familiar with using `for`

loops, comprehensions are like mini `for`

loops, and even have a similar syntax in Julia.

For example, the following is identical to `map(sqrt, a_vec)`

`sqrt(x) for x in a_vec] [`

```
5-element Vector{Float64}:
1.0
1.4142135623730951
1.7320508075688772
2.0
2.23606797749979
```

One exceptionally useful thing about comprehensions is that they can be combined with conditional evaluation, so that only things that match some boolean statement will be included. For example, the following only takes the square root of odd numbers:

`sqrt(x) for x in a_vec if isodd(x)] [`

```
3-element Vector{Float64}:
1.0
1.7320508075688772
2.23606797749979
```

We can also make dictionaries and other containers

```
# for reference
my_dict
```

```
Dict{Any, Any} with 4 entries:
"new key" => "😉"
"a key" => "a value"
'b' => 42
1 => 2
```

`Dict(k => my_dict[k] for k in keys(my_dict) if k isa String)`

```
Dict{String, String} with 2 entries:
"new key" => "😉"
"a key" => "a value"
```

You can do a lot in Julia without worrying too much about the `type`

s of the objects that you’re working with. But everything in `Julia`

has a type, and it’s good to be aware of them, if only to recognize errors that might show up due to them.

In Julia, types exist in a hierarchy. Every object has a “concrete” type, and some number of “abstract” parent types.

For example, `Int16`

, `Int32`

, and `Int64`

are concrete types representing 16-bit, 32-bit, and 64-bit integers respectively. All of these types are subtypes of the abstract type `Signed`

, which is itself a subtype of `Integer`

(there are also “unsigned” integer types, like `UInt64`

).

A `Float64`

is a 64-bit floating point number. It’s not a subtype of `Integer`

, but it shares the abstract type `Real`

with all `Integer`

types.

`typeof(1)`

`Int64`

`typeof(1.0)`

`Float64`

`supertype(Int64)`

`Signed`

Or view all of the supertypes:

```
using InteractiveUtils: supertypes
supertypes(Int64)
```

`(Int64, Signed, Integer, Real, Number, Any)`

`1.0 isa Integer`

`false`

`1.0 isa Float64`

`true`

`1.0 isa Real`

`true`

`1 isa Float64`

`false`

`1 isa Real`

`true`

Containers also have types, and in fact are generally “parameterized” based on the types they contain.

`= Dict('a' => 1, 'b' => 2, 'c' => 3) new_dict `

```
Dict{Char, Int64} with 3 entries:
'a' => 1
'c' => 3
'b' => 2
```

`typeof(new_dict)`

`Dict{Char, Int64}`

Notice the `Char`

and `Int64`

inside the curly braces - those represent the types of the keys and values respectively.

Why do I bring this up now? Well, look what happens when I try to add a new key / value pairs, without paying attention to the types:

`'d'] = 4.0 new_dict[`

`4.0`

`typeof(4.0)`

`Float64`

`typeof(new_dict['d'])`

`Int64`

`'e'] = 4.5 new_dict[`

`InexactError: InexactError(:Int64, Int64, 4.5)`

When I added the value `4.0`

, even though it was a `Float64`

, Julia was able to coerce it into an `Int64`

. But `4.5`

can’t be converted to an integer without losing information. we could explicitly round it, but Julia won’t do that for us.

`'e'] = round(Int, 4.5) new_dict[`

`4`

`"I'm a String, not a Char"] = 5 new_dict[`

`MethodError: MethodError(convert, (Char, "I'm a String, not a Char"), 0x00000000000082d1)`

So why was I able to add all kinds of different keys and values to `my_dict`

up above? Take a look at its type signature:

`typeof(my_dict)`

`Dict{Any, Any}`

In Julia, **all** types are subtypes of `Any`

. Because I initially made the dictionary with a bunch of different types, Julia could not provide it with a specific parameterization, so it just did the broadest possible one.

Caution

Here are some other examples of type issues in containers. Don’t worry too much about the details, but try to pay attention to what types you’d expect, what actually happens, and the errors that are (or are not!) induced:

`= [10, 11.0, 12] floatvec `

```
3-element Vector{Float64}:
10.0
11.0
12.0
```

`typeof(floatvec[1])`

`Float64`

`= Int64[10, 11.0, 12] intvec `

```
3-element Vector{Int64}:
10
11
12
```

`typeof(intvec[2])`

`Int64`

`= Any[10, 11.0, 12] anyvec `

```
3-element Vector{Any}:
10
11.0
12
```

`Int64[3, 3.5, 4]`

`InexactError: InexactError(:Int64, Int64, 3.5)`

`push!(intvec, 12.5)`

`InexactError: InexactError(:Int64, Int64, 12.5)`

`= 10 anum `

`10`

`typeof(anum)`

`Int64`

`push!(floatvec, anum)`

```
4-element Vector{Float64}:
10.0
11.0
12.0
10.0
```

`typeof(floatvec[4])`

`Float64`

`push!(intvec, '1') # 49`

```
4-element Vector{Int64}:
10
11
12
49
```

Caution

This one surprised me too! Character literals (like ‘1’) are based on the UTF-8 standard, where each character has a numerical value, which can be converted to an integer.

`push!(intvec, "1")`

`MethodError: MethodError(convert, (Int64, "1"), 0x00000000000082d1)`

`push!(anyvec, "1")`

```
4-element Vector{Any}:
10
11.0
12
"1"
```

`push!(intvec, parse(Int64, "1"))`

```
5-element Vector{Int64}:
10
11
12
49
1
```

Here are some additional bits that are useful to introduce at an early stage. You don’t need to keep these things in your head, but hopefully when you see them later, it will jog your memory.

Many “array-like” things in Julia aren’t actually arrays, but can be treated as such. This has a number of advantages.

For example, consider an array of odd numbers from 1 to 2,000,000. To put this into an array, you would need to store 1 million integer objects (assuming the typical 64-bit integer, that’s 8 Mb of memory).

Instead, you can store 3 integers in a “range”.

Tip

Writing `2,000,000`

would be parsed as a tuple `(2, 0, 0)`

, rather than as the integer 2 million. Instead, we can use `_`

for visual separation, which the Julia parser ignores in integers. So `2_000_000`

is identical to `2000000`

or `2_00000_0`

```
# range syntax for `start : step : stop`
= 1:2:2_000_000 my_range
```

`1:2:1999999`

This doesn’t actually materialize any of the numbers that are part of this range, but can still be indexed into, or used for indexing

`sizeof(my_range) # gives size in bytes`

`24`

`1000] # the thousandth number in the range my_range[`

`1999`

`1000, 1200, 11]] my_range[[`

```
3-element Vector{Int64}:
1999
2399
21
```

And some algorithms can use fancy tricks to optimize calculations. For example, `sum`

can use an optimization to calculate this almost instantly

```
using BenchmarkTools
@benchmark sum($my_range) # less than 5 nanoseconds
```

```
BenchmarkTools.Trial: 10000 samples with 1000 evaluations.
Range (min … max): 5.489 ns … 24.052 ns ┊ GC (min … max): 0.00% … 0.00%
Time (median): 5.500 ns ┊ GC (median): 0.00%
Time (mean ± σ): 5.560 ns ± 0.411 ns ┊ GC (mean ± σ): 0.00% ± 0.00%
██▄▅▂ ▅▁ ▂
██████▇▆▁▅▃▃▄▁▆▅▅▃▁▃▃▃▄▄▁▁▁▁▁▁▁▁▁▇███▇▄▃▃▁▁▁▃▁▁▁▃▁▄▄▃▁▁▁▁▃ █
5.49 ns Histogram: log(frequency) by time 6.02 ns <
Memory estimate: 0 bytes, allocs estimate: 0.
```

A range (and some other types) can work just like a vector because it is a subtype of `AbstractArray`

, and many functions don’t care about the internal details, they just care that they can get out indices, know the length of the object, etc. Many other “iterators” work the same way.

Nevertheless, sometimes you do actually need the concrete vector, in which case you can use the `collect()`

function:

`typeof(my_range)`

`StepRange{Int64, Int64}`

`= collect(my_range) range_as_vector `

`typeof(range_as_vector)`

`Vector{Int64} (alias for Array{Int64, 1})`

`sizeof(range_as_vector) # compare this to the 24 bytes used before`

`8000000`

`@benchmark sum($range_as_vector)`

```
BenchmarkTools.Trial: 10000 samples with 1 evaluation.
Range (min … max): 220.313 μs … 2.197 ms ┊ GC (min … max): 0.00% … 0.00%
Time (median): 221.999 μs ┊ GC (median): 0.00%
Time (mean ± σ): 224.189 μs ± 20.990 μs ┊ GC (mean ± σ): 0.00% ± 0.00%
▁▃▇█▇▅▃▁▁▁▁ ▁▁▂▁▁▁ ▁▂▂▃▃▄▃▃▃▃▂▁▁ ▂
▄▆▇█████████████▇▆▇▇████████████████████▇▇▆▆▅▆▅▅▅▇▇██████▇▇▇ █
220 μs Histogram: log(frequency) by time 234 μs <
Memory estimate: 0 bytes, allocs estimate: 0.
```

Sometimes, it can be convenient to chain functions together in a single line. For simple expressions, this can be done in Julia using the “pipe” operator `|>`

, which pipes the output from one expression into the input of the next. In other words, `x |> y`

is equivalent to `y(x)`

.

The following are equivalent:

```
|> collect |> sum
my_range
# and
sum(collect(my_range))
```

But this really only works for single-argument functions. As we’ll see, the `Chain.jl`

package can be used for more complex operations. With `Chain.jl`

, the result from each line of a calculation is passed implicitly as the first argument in the next.

```
using Chain
@chain my_range begin
collect
sumend
```

`1000000000000`

This is of course a trivial example, we’ll see much more complicated versions in future tutorials.