Loops

Just as any scientific programming language, Julia has different variants to implement loops. The perhaps most common one is the for loop

for i in 1:N
    # loop body
end

Here, Julia performs instructions inside the loop body for $i = 1, \ldots, N$. We can modify the iterates by for i in indexStart:increment:indexEnd. Hence, if we want to iterate from $N$ to $1$ with an increment of $2$, we have

for i in N:-2:1
    # loop body
end

If we want to iterate over a list or vector $v$, we can use for i in v. In this case, $i$ will take values in the vector $v$.

A further loop that can be used is the while loop, which performs a given instruction as long as a specified condition holds. Our previous example written as a while loop looks like this

while i <= N
    # loop body
    i = i - 2
end

using LinearAlgebra
# 1.
N = 5
A = zeros(N,N)

for i in 1:N
    for j in 1:N
        A[i, j] = (i - j)^2;
    end
end

# 2.
v = rand(N);
vNew = A * v / norm(A * v)

#3.
while norm(v - vNew) > 1e-5
    v .= vNew
    vNew .= A * v ./ norm(A * v)
end
#4.
println("Approximated dominant eigenvalue is $(norm(A * vNew))")

In order to stop a loop or skip an evaluation of the loop body at a specific iteration index, if a certain condition is fulfilled, we can use the break and continue commands. The break command will exit the loop. A simple example is

for i in 1:10
    if i > 5
        break
    end

    println("Iteration index is $i")
end

println("Loop stopped.")

Iteration index is 1
Iteration index is 2
Iteration index is 3
Iteration index is 4
Iteration index is 5
Loop stopped.

for i in 1:10    
    if i == 5
        continue
    end

    println("Iteration index is $i")
end

Iteration index is 1
Iteration index is 2
Iteration index is 3
Iteration index is 4
Iteration index is 6
Iteration index is 7
Iteration index is 8
Iteration index is 9
Iteration index is 10