Iterating

For Loops



In [2]:

    
for i = 1:4
    print(" $i ")
end



In [2]:

    
x = [10,20,40];
for i = x
    print(" $i ")
end



In [3]:

    
for i in x
    print(" $i ")
end



In [4]:

    
for i ∈ x
    print(" $i ")
end

Dictionaries



In [17]:

    
d = Dict( "foo" => 1, "bar" => 2 );
for i ∈ d
    println("$(i[1]) - $(i[2])")
end









    



bar - 2
foo - 1



In [20]:

    
d = Dict( "foo" => 1, "bar" => 2 );
for i ∈ keys(d)
    print(" $i ")
end









    



 bar  foo

Comprehensions



In [26]:

    
x = [2 * i % 3 for i in 1:3]









    Out[26]:





3-element Array{Int64,1}:
 2
 1
 0



In [28]:

    
x = [2 * i * j  for i in 2:3 , j in 1:5]









    Out[28]:





2×5 Array{Int64,2}:
 4   8  12  16  20
 6  12  18  24  30

While Loops



In [2]:

    
i = 0;
while i < 3
    print("yay! "); i=i+1;
end









    



yay! yay! yay!

Conditionals



In [3]:

    
x = 1;
if x > 2
    print("Great")
else
    print("Small")
end









    



Small



In [5]:

    
x = 3
x > 2 && print("Hello");
x > 4 && print("World");









    



Hello



In [7]:

    
x > 4 || print(":-)");

:-)

Excercises

Task 1

Calculate an approximation of $\pi$ using the "shotgun" approach from https://arxiv.org/abs/1404.1499 . Due to high risks involved with using actual shotguns, substitute the shotgun with the rand function. How many "shots" do you need to achieve an accuracy of 4 digits?



In [27]:

    
n = 10000000;
k = 1;
for i = 1:n
    x = rand(2);
    if norm(x) <= 1
        k = k + 1;
    end
end
k/n*4









    Out[27]:





3.14141

Task 2

Another approach for approximating π is to evaluate the sum $$ \pi \approx \pi_n = \sqrt{12} \sum_{k=0}^n \frac{(-3)^{-k}}{2k+1} $$ Determine the smallest value for $n$ such that $|\pi - \pi_n| < 10^{-15}$.



In [35]:

    
x = 0;
k = 0;
while abs(x-pi) >= 1e-15
    x = x + sqrt(12)*(-3.0)^-k / (2k+1)
    k = k + 1;
end
k-1









    Out[35]:





28

Task 3

Solve the first problem of project Euler, see https://projecteuler.net/problem=1 .



In [41]:

    
s = 0;
for i = 1:999
    if i % 3 == 0 || i % 5 == 0
        s = s + i
    end
end
s









    Out[41]:





233168