Introducing Julia/Controlling the flow

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Controlling the flow
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Types Functions

Different ways to control the flow[edit]

Typically each line of a Julia program is evaluated in turn. There are various ways to control and modify the flow of evaluation. These correspond with the constructs used in other languages:

  • ternary and compound expressions
  • Boolean switching expressions
  • if elseif else end - conditional evaluation
  • for end - iterative evaluation
  • while end - iterative conditional evaluation
  • try catch error throw exception handling
  • do blocks

Ternary expressions[edit]

Often you'll want to do job A (or call function A) if some condition is true, or job B (function B) if it isn't. The quickest way to write this is using the ternary operator ("?" and ":"):

julia> x = 1
1
julia> x > 3 ? "yes" : "no"
"no"
julia> x = 5
5
julia> x > 3 ? "yes" : "no"
"yes"

Here's another example:

julia> x = 0.3
0.3
julia> x < 0.5 ? sin(x) : cos(x)
0.29552020666133955

and Julia returned the value of sin(x), because x was less than 0.5. cos(x) wasn't evaluated at all.

Boolean switching expressions[edit]

Boolean operators let you evaluate an expression if a condition is true. You can combine the condition and expression using && or ||. && means "and", and || means "or". Since Julia evaluates expressions one by one, you can easily arrange for an expression to be evaluated only if a previous condition is true or false.

The following example uses a Julia function that returns true or false depending on whether the number is odd: isodd(n).

With &&, both parts have to be true, so we can write this:

julia> isodd(1000003) && @warn("That's odd!")
WARNING: That's odd!

julia> isodd(1000004) && @warn("That's odd!")
false

If the first condition (number is odd) is true, the second expression is evaluated. If the first isn't true, the expression isn't evaluated, and just the condition is returned.

With the || operator, on the other hand:

julia> isodd(1000003) || @warn("That's odd!")
true

julia> isodd(1000004) || @warn("That's odd!")
WARNING: That's odd!

If the first condition is true, there's no need to evaluate the second expression, since we already have the one truth value we need for "or", and it returns the value true. If the first condition is false, the second expression is evaluated, because that one might turn out to be true.

This type of evaluation is also called "short-circuit evaluation".

If and Else[edit]

For a more general — and traditional — approach to conditional execution, you can use if, elseif, and else. If you're used to other languages, don't worry about white space, braces, indentation, brackets, semicolons, or anything like that, but remember to finish the conditional construction with end.

julia> name = "Julia"
if name == "Julia"
   println("I like Julia")
elseif name == "Python"
   println("I like Python.")
   println("But I prefer Julia.")
else
   println("I don't know what I like")
end

The elseif and else parts are optional too:

julia> name = "Julia"
if name == "Julia"
   println("I like Julia")
end

Just don't forget the end!

How about 'switch' and 'case' statements? Well, you don't have to learn the syntax for those, because they don't exist!

ifelse[edit]

There's an ifelse function, too. It looks like this in action:

 julia> s = ifelse(false, "hello", "goodbye") * " world"

ifelse is an ordinary function, which evaluates all the arguments, and returns the second or third, depending on the value of the first. With the conditional if or ? ... :, only the expressions in the chosen route are evaluated.

For loops and iteration[edit]

Working through a list or a set of values or from a start value to a finish value are all examples of iteration, and the for ... end construction can let you iterate through a number of different types of object, including ranges, arrays, sets, dictionaries, and strings.

Here's the standard syntax for a simple iteration through a range of values:

julia> for i in 0:10:100
            println(i)
       end
0
10
20
30
40
50
60
70
80
90
100

The variable i takes the value of each element in the array (which is built from a range object) in turn — here stepping from 0 to 100 in steps of 10.

julia> for color in ["red", "green", "blue"] # an array
           print(color, " ")
       end
red green blue
julia> for letter in "julia" # a string
           print(letter, " ")
       end
j u l i a
julia> for element in (1, 2, 4, 8, 16, 32) # a tuple
           print(element, " ")
       end
1 2 4 8 16 32
julia> for i in Dict("A"=>1, "B"=>2) # a dictionary
       println(i)
       end
"B"=>2
"A"=>1
julia> for i in Set(["a", "e", "a", "e", "i", "o", "i", "o", "u"])
       println(i)
       end
e
o
u
a
i

We haven't yet met sets and dictionaries, but iterating through them is exactly the same.

You can iterate through a 2D array, stepping "down" through column 1 from top to bottom, then through column 2, and so on:

julia> a = reshape(1:100, (10, 10))
10x10 Array{Int64,2}:
  1  11  21  31  41  51  61  71  81   91
  2  12  22  32  42  52  62  72  82   92
  3  13  23  33  43  53  63  73  83   93
  4  14  24  34  44  54  64  74  84   94
  5  15  25  35  45  55  65  75  85   95
  6  16  26  36  46  56  66  76  86   96
  7  17  27  37  47  57  67  77  87   97
  8  18  28  38  48  58  68  78  88   98
  9  19  29  39  49  59  69  79  89   99
 10  20  30  40  50  60  70  80  90  100

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

You can use = instead of in.

Iterating over an array and updating it[edit]

When you're iterating over an array, the array is checked each time through the loop, in case it's changed. A mistake you should avoid making is to use push! to make an array grow in the middle of a loop. Run the following text carefully, and be ready to Ctrl-C when you've seen enough (otherwise your computer will eventually crash):

 julia> c = [1]
 1-element Array{Int64,1}:
  1
 
 julia> for i in c
           push!(c, i)
           @show c
           sleep(1)
       end
 c = [1,1]
 c = [1,1,1]
 c = [1,1,1,1]
 ...

Loop variables and scope[edit]

The variable that steps through each item — the 'loop variable' will disappear as soon as the loop finishes.

julia> for i in 1:10 
     @show i 
 end 
i = 1
i = 2
i = 3
i = 4
i = 5
i = 6
i = 7
i = 8
i = 9
i  = 10

julia> i
ERROR: UndefVarError: i not defined

If you want to remember the value of the loop variable outside the loop (eg if you had to exit the loop and needed to know the value you'd reached), use the global keyword to define a variable that outlasts the loop.

julia> for i in 1:10
     global howfar 
     if i % 4 == 0 
         howfar = i 
     end 
 end 
julia> howfar
8

Here, howfar didn't exist before the loop, but it survived to tell its story.

Variables declared inside a loop[edit]

In a similar way, if you declare a new variable inside a loop, it won't exist once the loop finishes. In this example, k is created inside:

julia> for i in 1:5
     k = i^2 
     println("$(i) squared is $(k)")
 end 
1 squared is 1
2 squared is 4
3 squared is 9
4 squared is 16
5 squared is 25

and doesn't exist immediately after the loop finishes:

julia> k
ERROR: UndefVarError: k not defined

Variables created inside a loop are forgotten at the end of each iteration. Look at the following loop:

for i in 1:10
    if ! @isdefined z
        println("z isn't defined")
    end
    z = i
    println("z is $z")
end

Perhaps you expected only the first loop to produce the "z isn't defined error"? In fact, even if z is created in the body of the loop, it is undefined at the start of the next iteration.

z isn't defined
z is 1
z isn't defined
z is 2
z isn't defined
z is 3
z isn't defined
z is 4
z isn't defined
z is 5
z isn't defined
z is 6
z isn't defined
z is 7
z isn't defined
z is 8
z isn't defined
z is 9
z isn't defined
z is 10

You can use the global keyword to force z to be available outside the loop once it's been created:

for i in 1:10
    global z
    if ! @isdefined z
        println("z isn't defined")
    else
        println("z was $z")
    end
    z = i
    println("z is $z")
end
z isn't defined
z is 1
z was 1
z is 2
z was 2
...
z is 9
z was 9
z is 10

although, if you're working in global scope, z is now available everywhere, with the value 10.

Better practice is to contain variables inside functions:

function test()
    for i in 1:10
        local z = i
        if ! @isdefined z
            println("z isn't defined")
        else
            println("z was $z")
        end
        z = i
        println("z is $z")
    end
end
julia> test()
z was 1
z is 1
z was 2
z is 2
...z was 10
z is 10

and now z will be available inside the function and the loop. This z will have no connection with any similarly named variables outside the function.

Fine tuning the loop: Continue[edit]

Sometimes on a particular iteration you might want to skip to the next value. You can use continue to skip the rest of the code inside the loop and start the loop again with the next value.

julia> for i in 1:10
    if i % 3 == 0
       continue
    end
    println(i) # this and subsequent lines are
               # skipped if i is a multiple of 3
end

1
2
4
5
7
8
10

Comprehensions[edit]

This oddly-named concept is simply a way of generating and collecting items. In mathematical circles you would say something like this:

"Let S be the set of all elements n where n is greater than or equal to 1 and less than or equal to 10". 

In Julia, you can write this as:

 julia> S = Set([n for n in 1:10])
Set([7,4,9,10,2,3,5,8,6,1])

and the [n for n in 1:10] construction is called array comprehension or list comprehension ('comprehension' in the sense of 'getting everything' rather than 'understanding'). The outer brackets collect together the elements generated by evaluating the expression placed before the for iteration. Instead of end, use a square bracket to finish.

julia> [i^2 for i in 1:10]
10-element Array{Int64,1}:
   1
   4
   9
  16
  25
  36
  49
  64
  81
 100

The type of elements can be specified:

julia> Complex[i^2 for i in 1:10]
10-element Array{Complex,1}:
   1.0+0.0im
   4.0+0.0im
   9.0+0.0im
  16.0+0.0im
  25.0+0.0im
  36.0+0.0im
  49.0+0.0im
  64.0+0.0im
  81.0+0.0im
 100.0+0.0im

But Julia can work out the types of the results you're producing:

julia> [(i, sqrt(i)) for i in 1:10]
10-element Array{Tuple{Int64,Float64},1}:
 (1,1.0)
 (2,1.41421)
 (3,1.73205)
 (4,2.0)
 (5,2.23607)
 (6,2.44949)
 (7,2.64575)
 (8,2.82843)
 (9,3.0)
 (10,3.16228)

Here's how to make a dictionary via comprehension:

julia> Dict(string(Char(i + 64)) => i for i in 1:26)
Dict{String,Int64} with 26 entries:
  "Z" => 26
  "Q" => 17
  "W" => 23
  "T" => 20
  "C" => 3
  "P" => 16
  "V" => 22
  "L" => 12
  "O" => 15
  "B" => 2
  "M" => 13
  "N" => 14
  "H" => 8
  "A" => 1
  "X" => 24
  "D" => 4
  "G" => 7
  "E" => 5
  "Y" => 25
  "I" => 9
  "J" => 10
  "S" => 19
  "U" => 21
  "K" => 11
  "R" => 18
  "F" => 6

Next, here are two iterators in a comprehension, separated with a comma, which makes generating tables very easy. Here we're making a tuple-table:

julia> [(r,c) for r in 1:5, c in 1:2]
5×2 Array{Tuple{Int64,Int64},2}:
 (1,1)  (1,2)
 (2,1)  (2,2)
 (3,1)  (3,2)
 (4,1)  (4,2)
 (5,1)  (5,2)

r goes through five cycles, one cycle for every value of c. Nested loops work in the opposite manner. Here the column-major order is respected, as shown when the array is filled with nanosecond time values:

julia> [Int(time_ns()) for r in 1:5, c in 1:2]
5×2 Array{Int64,2}:
 1223184391741562  1223184391742642
 1223184391741885  1223184391742817
 1223184391742067  1223184391743009
 1223184391742256  1223184391743184
 1223184391742443  1223184391743372

You can supply a test expression as well to filter the production. For example, produce all the integers between 1 and 100 that are exactly divisible by 7:

julia> [x for x in 1:100 if x % 7 == 0]
14-element Array{Int64,1}:
  7
 14
 21
 28
 35
 42
 49
 56
 63
 70
 77
 84
 91
 98
Generator expressions[edit]

Like comprehensions, generator expressions can be used to produce values from iterating a variable, but, unlike comprehensions, the values are produced on demand.

julia> sum(x^2 for x in 1:10)
385
julia> collect(x for x in 1:100 if x % 7 == 0)
14-element Array{Int64,1}:
  7
 14
 21
 28
 35
 42
 49
 56
 63
 70
 77
 84
 91
 98

Enumerating arrays[edit]

Often you want to go through an array element by element while also keeping track of the index number of each element. The enumerate() function gives you an iterable version of something, producing both an index number and the value at each index number:

julia> m = rand(0:9, 3, 3)
3×3 Array{Int64,2}:
 6  5  3
 4  0  7
 1  7  4

julia> [i for i in enumerate(m)]
3×3 Array{Tuple{Int64,Int64},2}:
 (1, 6)  (4, 5)  (7, 3)
 (2, 4)  (5, 0)  (8, 7)
 (3, 1)  (6, 7)  (9, 4)

The array is checked for possible changes at each iteration of the loop.

Zipping arrays[edit]

Sometimes you want to work through two or more arrays at the same time, taking the first element of each array first, then the second, and so on. This is possible using the well-named zip() function:

julia> for i in zip(0:10, 100:110, 200:210)
     println(i)
end
(0,100,200)
(1,101,201)
(2,102,202)
(3,103,203)
(4,104,204)
(5,105,205)
(6,106,206)
(7,107,207)
(8,108,208)
(9,109,209)
(10,110,210)

You'd think it would all go wrong if the arrays were different sizes. What if the third array is too big, or too small?

julia> for i in zip(0:10, 100:110, 200:215)
    println(i)
end
(0,100,200)
(1,101,201)
(2,102,202)
(3,103,203)
(4,104,204)
(5,105,205)
(6,106,206)
(7,107,207)
(8,108,208)
(9,109,209)
(10,110,210)

but Julia isn't fooled — any oversupply or undersupply in any one of the arrays is handled gracefully.

julia> for i in zip(0:15, 100:110, 200:210)
    println(i)
end
(0,100,200)
(1,101,201)
(2,102,202)
(3,103,203)
(4,104,204)
(5,105,205)
(6,106,206)
(7,107,207)
(8,108,208)
(9,109,209)
(10,110,210)

Iterable objects[edit]

The "for something in something" construction is the same for everything that you can iterate through: arrays, dictionaries, strings, sets, ranges, and so on. In Julia this is a general principle: there are a number of ways in which you can create an "iterable object", an object that is designed to be used as part of the iteration process that provides the elements one at a time.

The most obvious example we've already met is the range object. It doesn't look much when you type it into the REPL:

julia> ro = 0:2:100
0:2:100

But it yields the numbers on demand, when you start iterating:

julia> [i for i in ro]
51-element Array{Int64,1}:
   0
   2
   4
   6
   8
  10
  12
  14
  16
  18
  20
  22
  24
  26
  28
   
  74
  76
  78
  80
  82
  84
  86
  88
  90
  92
  94
  96
  98
 100

Should you want the actual numbers from a range (or other iterable object), you can use collect():

julia> collect(0:25:100)
5-element Array{Int64,1}:
   0
  25
  50
  75
 100

This might be helpful when you have iterable objects created by other Julia functions. For example, permutations() creates an iterable object containing all the permutations of an array. You could use collect() to grab them and make a new array:

julia> collect(permutations(1:4))
24-element Array{Array{Int64,1},1}:
 [1,2,3,4]
 [1,2,4,3]
 
 [4,3,2,1]

but on anything large there are going to hundreds of permutations. And that's the reason why iterator objects don't produce all the values from the iteration at the same time: memory and performance. A range object doesn't take up much room, even if iterating over it might take ages, depending on how big the range is. If you generate all the numbers at once, rather than only producing them when they're needed, they all have to be stored somewhere until you need them…

Julia provides iterable objects for working with other types of data. For example, when you're working with files, you can treat an open file as an iterable object:

 filehandle = "/Users/me/.julia/logs/repl_history.jl"
 for line in eachline(filehandle)
     println(length(line), line)
 end
Use eachindex()[edit]

A common pattern when iterating through arrays is to perform some task for each value of i, where i is the index number of each element, not the element:

 for i = 1:length(A) 
   # do something with i or A[i]
 end

There is a more efficient (i.e. faster in some situations) way to do this:

 for i in eachindex(A) 
   # do something with i or A[i]
 end

Even more iterators[edit]

There's a Julia package called Iterators.jl that provides some advanced iterator functions.

 julia> using Iterators

For example, partition() groups the objects in the iterator into easily-handled chunks:

 collect(partition(1:10, 3, 1))
8-element Array{Tuple{Int64,Int64,Int64},1}:
 (1, 2, 3) 
 (2, 3, 4) 
 (3, 4, 5) 
 (4, 5, 6) 
 (5, 6, 7) 
 (6, 7, 8) 
 (7, 8, 9) 
 (8, 9, 10)

chain() works through all the iterators one after the other:

 for i in chain(1:3, ['a', 'b', 'c'])
   @show i
end

 i = 1
 i = 2
 i = 3
 i = 'a'
 i = 'b'
 i = 'c'

subsets() works through all subsets of an object. You can specify a size:

 for i in subsets(collect(1:6), 3)
   @show i
end

 i = [1,2,3]
 i = [1,2,4]
 i = [1,2,5]
 i = [1,2,6]
 i = [1,3,4]
 i = [1,3,5]
 i = [1,3,6]
 i = [1,4,5]
 i = [1,4,6]
 i = [1,5,6]
 i = [2,3,4]
 i = [2,3,5]
 i = [2,3,6]
 i = [2,4,5]
 i = [2,4,6]
 i = [2,5,6]
 i = [3,4,5]
 i = [3,4,6]
 i = [3,5,6]
 i = [4,5,6]

Making your own iterable objects[edit]

It's possible to design your own iterable objects. When you're defining your type, you add a couple of methods to Julia's iterate() function. Then you can use something like for .. end loop to work through the components of your object, and these iterate() methods are called automatically as necessary.

The following example shows how you can create an iterable object that iterates through prime numbers, starting at 1, going up to a certain value.

(The isprime() function lives in an external package called Primes, so before starting this section, you must add it and import it.)

 using Primes

First, you define a new type that will be a prime iterator:

struct PrimeIterator
    n::Integer
end

You will later create an iterable object of this type using something like this:

 primesupto20 = PrimeIterator(20)

The number you supply is passed to the type constructor, and stored in n. The iterator will be expected to generate every prime up to this number but no further.

So to define what happens when you try to iterate this type, you must add two methods to the iterate() function. This function already exists in Julia (that's why you can iterate over all the basic data objects), so the Base prefix is required: you're adding a new method to the existing iterate() function, one which is designed to handle these special objects.

The first method takes no arguments, except for the type, and is for starting the iteration process off.

function Base.iterate(::PrimeIterator)
    return (1, 2)
end

It returns a tuple: the first value, and the next state of the iterator.

Next, you add a iterate(type, state) method to Julia's iterate() function. This takes two arguments, an iterable object and the current state, and returns a tuple of two values, the next item and the next state. But, if there are no more values available, the iterate() function should return nothing.

function Base.iterate(piter::PrimeIterator, state)
    if state >= piter.n
        return 
    end    
    while ! isprime(state)
        state += 1
    end
    return (state, state += 1)
end

Telling the iterator when it's finished is easy in this case, because the construction of the PrimeIterator object expected a number, which acts as the stop point. And, because this number was called n in the type definition, it can be accessed using the "." field accessor. This is the only time you refer to the original number which was passed to the constructor.

With these two methods added for the PrimeIterator type, it's now possible to iterate through our prime iterator objects, eg from 1 to 20:

 primesupto20 = PrimeIterator(20)

for i in primesupto20
    println(i)
end

1
2
3
5
7
11
13
17
19

As you add more methods that handle PrimeIterator objects, you can use more and more Julia functions with it. For example, if you add a length method:

function Base.length(piter::PrimeIterator)
    return piter.n
end

then Julia's length() function knows how long PrimeIterators are:

julia> length(primesupto20)
20

For some types (but perhaps not so easy for prime numbers), you can add a getindex() method to Julia's getindex() function. This allows you to make use of the array indexing notation to find the nth prime.

We'll cheat a bit by using Primes.jl to calculate the primes.

function Base.getindex(pi::PrimeIterator, i::Int)
    1 <= i < length(pi) || throw(BoundsError(pi, i))
    i == 1 && return 1
    return primes(pi.n)[i-1]
end

This lets us do this:

julia> primesupto20[1]
1

julia> primesupto20[2]
2

julia> primesupto20[3]
3

julia> primesupto20[8]
17

julia> primesupto20[9]
19

(Code inspired by Carl Vogel posts at [1].)

Nested loops[edit]

If you want to nest one loop inside another, you don't have to duplicate the for and end keywords. Just use a comma:

julia> for x in 1:10, y in 1:10
          @show (x, y)
       end
(x,y) = (1,1)
(x,y) = (1,2)
(x,y) = (1,3)
(x,y) = (1,4)
(x,y) = (1,5)
(x,y) = (1,6)
(x,y) = (1,7)
(x,y) = (1,8)
(x,y) = (1,9)
(x,y) = (1,10)
(x,y) = (2,1)
(x,y) = (2,2)
(x,y) = (2,3)
(x,y) = (2,4)
(x,y) = (2,5)
(x,y) = (2,6)
(x,y) = (2,7)
(x,y) = (2,8)
(x,y) = (2,9)
(x,y) = (2,10)
(x,y) = (3,1)
(x,y) = (3,2)
...
(x,y) = (9,9)
(x,y) = (9,10)
(x,y) = (10,1)
(x,y) = (10,2)
(x,y) = (10,3)
(x,y) = (10,4)
(x,y) = (10,5)
(x,y) = (10,6)
(x,y) = (10,7)
(x,y) = (10,8)
(x,y) = (10,9)
(x,y) = (10,10)

(The useful @show macro prints out the names of things and their values.)

One difference between the shorter and longer forms of nesting loops is the behaviour of break:

julia> for x in 1:10
          for y in 1:10
              @show (x, y)
              if y % 3 == 0
                 break
              end
          end
       end
(x,y) = (1,1)
(x,y) = (1,2)
(x,y) = (1,3)
(x,y) = (2,1)
(x,y) = (2,2)
(x,y) = (2,3)
(x,y) = (3,1)
(x,y) = (3,2)
(x,y) = (3,3)
(x,y) = (4,1)
(x,y) = (4,2)
(x,y) = (4,3)
(x,y) = (5,1)
(x,y) = (5,2)
(x,y) = (5,3)
(x,y) = (6,1)
(x,y) = (6,2)
(x,y) = (6,3)
(x,y) = (7,1)
(x,y) = (7,2)
(x,y) = (7,3)
(x,y) = (8,1)
(x,y) = (8,2)
(x,y) = (8,3)
(x,y) = (9,1)
(x,y) = (9,2)
(x,y) = (9,3)
(x,y) = (10,1)
(x,y) = (10,2)
(x,y) = (10,3)

julia> for x in 1:10, y in 1:10
          @show (x, y)
         if y % 3 == 0
           break
         end
       end
(x,y) = (1,1)
(x,y) = (1,2)
(x,y) = (1,3)

Notice that break breaks out of both inner and outer loops in the shorter form, but only out of the inner loop in the longer form.

Optimizing nested loops[edit]

With Julia, the inner loop should concern rows rather than columns. This is due to how arrays are stored in memory.

The following examples consist of simple loops, but the way the rows and columns are iterated differ. The "bad" version jumps across from column to column, which means calculating the jump each time. In other words, it looks at every column of a row, then at every column of the next row, and so on:

function laplacian_bad(lap_x::Array{Float64,2}, x::Array{Float64,2})
    nr,nc = size(x)
    for ir = 2:nr-1, ic = 2:nc-1 # bad loop nesting order
        lap_x[ir,ic] =
            (x[ir+1,ic] + x[ir-1,ic] +
            x[ir,ic+1] + x[ir,ic-1]) - 4*x[ir,ic]
    end
end

In the "good" version, the two loops are nested properly:

function laplacian_good(lap_x::Array{Float64,2}, x::Array{Float64,2})
    nr,nc = size(x)
    for ic = 2:nc-1, ir = 2:nr-1 # good loop nesting order
        lap_x[ir,ic] =
            (x[ir+1,ic] + x[ir-1,ic] +
            x[ir,ic+1] + x[ir,ic-1]) - 4*x[ir,ic]
    end
end

Another way to increase the speed is to remove the array bounds checking, using the macro @inbounds:

function laplacian_good_nocheck(lap_x::Array{Float64,2}, x::Array{Float64,2})
    nr,nc = size(x)
    for ic = 2:nc-1, ir = 2:nr-1 # good loop nesting order
        @inbounds begin lap_x[ir,ic] = # no array bounds checking
            (x[ir+1,ic] +  x[ir-1,ic] +
            x[ir,ic+1] + x[ir,ic-1]) - 4*x[ir,ic]
        end
    end
end

Here's the test function:

function main_test(nr, nc)
    field = zeros(nr, nc)
    for ic = 1:nc, ir = 1:nr
        if ir == 1 || ic == 1 || ir == nr || ic == nc
            field[ir,ic] = 1.0
        end
    end
    lap_field = zeros(size(field))

    time = @elapsed laplacian_bad(lap_field, field)
    @printf "laplacian_bad:          %.3f s\n" time
    
    time = @elapsed laplacian_good(lap_field, field)
    @printf "laplacian_good:         %.3f s\n" time
    
    time = @elapsed laplacian_good_nocheck(lap_field, field)
    @printf "laplacian_good_nocheck: %.3f s\n" time
end

and the results show the difference in performance just based on the row/column scanning order. The "no check" version is even faster....

julia> main_test(10000,10000)
laplace_bad:          3.209 s
laplace_good:         0.436 s
laplace_good_nockeck: 0.157 s

While loops[edit]

To repeat some expressions while a condition is true, use the while ... end construction.

julia> x = 0
0
julia> while x < 4
    println(x)
    x += 1
end

0
1
2
3

If you want the condition to be tested after the statements, rather than before, producing a "do .. until" form, use the following construction:

while true
   println(x)
   x += 1
   x >= 4 && break
end

0
1
2
3

Here we're using a Boolean switch rather than an if ... end statement.

Using Julia's macros, you can create your own control structures. See Metaprogramming.

Exceptions[edit]

If you want to write code that checks for errors and handles them gracefully, use the try ... catch construction.

With a catch phrase, you can handle problems that occur in your code, possibly allowing the program to continue rather than grind to a halt.

In the next example, our code attempts to change the first character of a string directly (which isn't allowed, because strings in Julia can't be modified in place):

julia> s = "string";
julia> try
          s[1] = "p"
       catch e
          println("caught an error $e")
          println("but we can continue with execution")
       end

caught an error <code>MethodError(setindex!,("string","p",1))</code> but we can continue with execution

The error() function raises an error exception with a given message.

Do block[edit]

Finally, let's look at a do block, which is another syntax form that, like the list comprehension, looks at first sight to be a bit backwards (i.e. it can perhaps be better understood by starting at the end and working towards the beginning).

Remember the find() example from earlier?

julia> smallprimes = [1,2,3,5,7,11,13,17,19,23];

julia> findall(x -> isequal(13, x), smallprimes)
1-element Array{Int64,1}:
 7

The anonymous function (x -> x isequal(13, x)) is the first argument of find(), and operates on the second. But with a do block, you can lift the function out and put it in between a do ... end block construction:

julia> findall(smallprimes) do x
                 isequal(x, 13)
           end
1-element Array{Int64,1}:
 7

You just lose the arrow and change the order, putting the find() function and its target argument first, then adding the anonymous function's arguments and body after the do.

The idea is that it's easier to write a longer anonymous function on multiple lines at the end of the form, rather than wedged in as the first argument.