Common Data Structures
Contents
Common Data Structures¶
Arrays¶
Array’s are N-dimensional data structures of a common type (the type could be Any). The type signature is
Array{T, N}
where T is the type and N is the dimension. You can omit N and it will be inferred for the arguments
Array{Any, 3}(nothing, 3, 2, 3)
3×2×3 Array{Any, 3}:
[:, :, 1] =
nothing nothing
nothing nothing
nothing nothing
[:, :, 2] =
nothing nothing
nothing nothing
nothing nothing
[:, :, 3] =
nothing nothing
nothing nothing
nothing nothing
x = Array{Any}(nothing, 2, 3)
2×3 Matrix{Any}:
nothing nothing nothing
nothing nothing nothing
A Vector is an Array with N=1, a Matrix is an Array with N=2.
Vector{Float64}(undef, 3)
3-element Vector{Float64}:
0.0
6.91051096480046e-310
6.91054319031837e-310
Matrix{Float64}(undef, 3, 3)
3×3 Matrix{Float64}:
6.4e-323 3.0e-323 1.0e-323
3.5e-323 2.0e-323 5.0e-324
2.5e-323 1.5e-323 6.91054e-310
Float64[1.0, 2.0, 3.0]
3-element Vector{Float64}:
1.0
2.0
3.0
y = Float64[1.0 2.0 3.0; 4.0 5.0 6.0]
2×3 Matrix{Float64}:
1.0 2.0 3.0
4.0 5.0 6.0
Array indexing and assignment¶
y[1, 2]
2.0
y[1:2, 2]
2-element Vector{Float64}:
2.0
5.0
y[end,end] = 100;
y
2×3 Matrix{Float64}:
1.0 2.0 3.0
4.0 5.0 100.0
x[1, 1] = "test"
x[2, 1:3] .= 1
x
2×3 Matrix{Any}:
"test" nothing nothing
1 1 1
Views¶
z = y[1:2, 1:2]
2×2 Matrix{Float64}:
1.0 2.0
4.0 5.0
z[1,1] = 100.0
@show z
@show y;
z = [100.0 2.0; 4.0 5.0]
y = [1.0 2.0 3.0; 4.0 5.0 100.0]
z = @view y[1:2, 1:2]
z[1, 1] = 100.0
y
2×3 Matrix{Float64}:
100.0 2.0 3.0
4.0 5.0 100.0
Convenience constructors¶
zeros(Int32, 2, 3)
2×3 Matrix{Int32}:
0 0 0
0 0 0
zeros(2, 3)
2×3 Matrix{Float64}:
0.0 0.0 0.0
0.0 0.0 0.0
ones(2, 3)
2×3 Matrix{Float64}:
1.0 1.0 1.0
1.0 1.0 1.0
fill(77.0, 2, 2)
2×2 Matrix{Float64}:
77.0 77.0
77.0 77.0
fill!(y, 22.0)
2×3 Matrix{Float64}:
22.0 22.0 22.0
22.0 22.0 22.0
Operations on arrays¶
Multiplication of a Matrix and a Vector automatically does matrix multiplication.
@show y
@show x = [1.0, 2.0, 3.0]
y * x
y = [22.0 22.0 22.0; 22.0 22.0 22.0]
x = [1.0, 2.0, 3.0] = [1.0, 2.0, 3.0]
2-element Vector{Float64}:
132.0
132.0
If we want element-wise multiplication we need to use .*.
x .* x
3-element Vector{Float64}:
1.0
4.0
9.0
Addition/subtraction of two Arrays of the same size gives element-wise addition.
x + x
3-element Vector{Float64}:
2.0
4.0
6.0
We can broadcast the addition operation along matching dimensions of Arrays.
@show size(y')
@show size(x)
y' .+ x
size(y') = (3, 2)
size(x) = (3,)
3×2 Matrix{Float64}:
23.0 23.0
24.0 24.0
25.0 25.0
Any scalar operation can be vectorized with the . operator, i.e.
my_scalar_operation(x, y) = x * y + x^2 * y^2
my_scalar_operation(1.0, 2.0)
6.0
my_scalar_operation.([1.0, 2.0, 3.0], [4.0, 5.0, 6.0])
3-element Vector{Float64}:
20.0
110.0
342.0
Array functions¶
There are numerous array functions such as sum, cumsum, prod, etc. For example
accumulate(+, [1, 2, 3])
3-element Vector{Int64}:
1
3
6
See Array documentation for more examples.
Tuples¶
Tuples are fixed length containers that can hold any values, but cannot be modified (they are immutable).
x = ("a string", 1.0, 33)
("a string", 1.0, 33)
x[1]
"a string"
x[2] = 2.0
MethodError: no method matching setindex!(::Tuple{String, Float64, Int64}, ::Float64, ::Int64)
Stacktrace:
[1] top-level scope
@ In[28]:1
[2] eval
@ ./boot.jl:373 [inlined]
[3] include_string(mapexpr::typeof(REPL.softscope), mod::Module, code::String, filename::String)
@ Base ./loading.jl:1196
Named Tuples¶
x = (a = "a string", b = 1.0, c = 33)
(a = "a string", b = 1.0, c = 33)
@show x[1]
@show x.a;
x[1] = "a string"
x.a = "a string"
_, bb, _ = x
@show bb;
bb = 1.0
Dictionaries¶
Dictionaries are data structures to store and lookup key-value pairs, i.e.
dict = Dict("a" => "a string", "b" => 33, "name" => "John")
@show dict["b"]
@show dict["name"];
dict["b"] = 33
dict["name"] = "John"
They can also be constructed using a collection of tuples.
dict = Dict([("a","a string"), ("b", 33), ("name", "John")])
@show dict["b"]
@show dict["name"];
dict["b"] = 33
dict["name"] = "John"