Control Flow

The for loop

To iterate over the elements within an array, there are several different ways to write the code. Now suppose we have such an array: a = copy(reshape(1:16, 4, 4))

4×4 Matrix{Int64}:
 1  5   9  13
 2  6  10  14
 3  7  11  15
 4  8  12  16

1. eachindex(a)

In Julia, matrices are stored column-first. Hence, eachindex() iterates over matrix a in column order.

• eachindex() returns the index of each element of a matrix, of type Int

for i in eachindex(a)
    println("Index: $i, Element: $(a[i])")
end

Index: 1, Element: 1
Index: 2, Element: 2
Index: 3, Element: 3
Index: 4, Element: 4
Index: 5, Element: 5
Index: 6, Element: 6
...

2. a

• in a returns each element of a matrix, of type eltype(a)

for element in a
    println("Element: $element")
end

3. pairs(a)

The pairs() function, when used as an iterator, can iterate not only over arrays, but also over Pairs and dictionaries.

• pairs(a::Vector) returns a pair of index and value, of type Tuple{Int,eltype(a)}
• pairs(a::Matrix) returns a pair of index and value, of type Tuple{CartesianIndex{2},eltype(a)}
• pairs(::Dict) returns a pair of key and value, of type Tuple{eltype(a.keys),eltype(a.vals)}

A [println("Index: $i, Element: $element") for (i, element) in pairs(a)] gives:

Index: CartesianIndex(1, 1), Element: 1
Index: CartesianIndex(2, 1), Element: 2
Index: CartesianIndex(3, 1), Element: 3
Index: CartesianIndex(4, 1), Element: 4
Index: CartesianIndex(1, 2), Element: 5
Index: CartesianIndex(2, 2), Element: 6
...

4. enumerate(a)

The first parameter i produced by enumerate is the index of natural number starting from 1.

A [println("Index: $i, Element: $element") for (i, element) in enumerate(a)] gives:

Index: 1, Element: 1
Index: 2, Element: 2
Index: 3, Element: 3
Index: 4, Element: 4
Index: 5, Element: 5
Index: 6, Element: 6
...

5. axes(a,n)

This function iterates over the nth axis of array a.

for element in axes(a, 1)
    println("Element: $element")
end

Element: 1
Element: 2
Element: 3
Element: 4

Creating Iterators

An iterator can be created using parentheses wrapped around an array and a for loop -> (a[i] for i in a)

For example, we can create a row index iterator for matrix x:

x = rand(1000, 4);
eachrow_x = (x[i:i, :] for i in axes(x, 1));
eachrow_x = (view(x, i:i, :) for i in axes(x, 1));
eachrow_x = eachrow(x);
for (i, xi) in enumerate(eachrow_x)
    println("Index: $i, Element: $element")
    xi[1] = 0.0
end

• Line 2 let the for loop performs a slicing operation on the matrix x at each iteration, producing a new vector for which a memory allocation occurs.

• Lines 3 and 4 are equivalent iterators that let the for loop produce a row view of the matrix x per iteration. No memory allocation.