how do we represent the model?

# Random notes.

use a vector (closest to numpy arrays)

homeogenous containers

[2,3,24.0]

3-element Vector{Float64}:
  2.0
  3.0
 24.0

[3,23, "ji"] # avoid vectors of any type

3-element Vector{Any}:
  3
 23
   "ji"

model = [0.3, 0.96, 4, 0.1, 0.4]

5-element Vector{Float64}:
 0.3
 0.96
 4.0
 0.1
 0.4

# to access variables I need to remembeer the positions
I_alpha = 1
model[I_alpha]

0.3

# a tuple 
# positional container that is immutable
model = (0.3, 0.96, 4, 0.1, 0.4)

(0.3, 0.96, 4, 0.1, 0.4)

model[1]

0.3

model[2] = 43

MethodError: MethodError: no method matching setindex!(::Tuple{Float64, Float64, Int64, Float64, Float64}, ::Int64, ::Int64)
The function `setindex!` exists, but no method is defined for this combination of argument types.
MethodError: no method matching setindex!(::Tuple{Float64, Float64, Int64, Float64, Float64}, ::Int64, ::Int64)

The function `setindex!` exists, but no method is defined for this combination of argument types.



Stacktrace:

 [1] top-level scope

   @ ~/Teaching/econobits/eco309/corrections/jl_notebook_cell_df34fa98e69747e1a8f8a730347b8e2f_X12sZmlsZQ==.jl:1

numbers = [1.0, 2.0, 4.0, 8.0]

4-element Vector{Float64}:
 1.0
 2.0
 4.0
 8.0

[x^2 for x in numbers if x<5]

3-element Vector{Float64}:
  1.0
  4.0
 16.0

it = (x^2 for x in numbers)

Base.Generator{Vector{Float64}, var"#50#51"}(var"#50#51"(), [1.0, 2.0, 4.0, 8.0])

sum(it)

85.0

# tuples a more memory efficient than vectors
numbers = [1.0, 2.0, 4.0, 8.0]
function fun1(x, numbers)
    res = sum( (x^2 for x in numbers) )
    return res
end

fun1 (generic function with 2 methods)

@time fun1(2, numbers)

  0.000006 seconds (1 allocation: 16 bytes)

85.0

# tuples a more memory efficient than vectors
numbers = (1.0, 2.0, 4.0, 8.0)
function fun2(x, numbers)
    res = sum( (x^2 for x in numbers) )
    return res
end

fun2 (generic function with 1 method)

@time fun2(2, numbers)

  0.000007 seconds (1 allocation: 16 bytes)

85.0

# tuples share the same issues as vecotrs
# position sensitive

# a dictionary (list of pairs)

# d = Dict(
#     "α"=>0.3,
#     "β"=>0.96,
#     "γ"=>4.0,
#     "δ"=>0.1
# )

# d["α"]

# use small-strings (symbols) that are optimized

d = Dict(
    :α=>0.3,
    :β=>0.96,
    :γ=>4.0,
    :δ=>0.1
)

d[:α]

0.3

# idctionaries are not memory efficient
# they can grow, contain any kind of data...

define your own structure

struct Model{T}
    α::Float64
    β::Float64
    γ::Float64
    δ::Float64
end

# instantiate
m = Model(0.3, 0.96, 4.0, 0.1)

Model(0.3, 0.96, 4.0, 0.1)

sizeof(m)

# advantages
# - memorey efficeint
# - easy to acces fields

m.α

0.3

# problems:
# - still need to remember the positions when creating the object
#      # workaround @kwdef
# - can't change easily the structure definition

Namedtuples

m = (; α=0.3, β=0.97, γ=4.0, δ=0.1, s=0.2)   # ; is followed by keywords

(α = 0.3, β = 0.97, γ = 4.0, δ = 0.1, s = 0.2)

m[1] # behaves like a tuple (is memory efficient)

0.3

m.α

0.3

range(1,10 ;  length=100)

1.0:0.09090909090909091:10.0

# named unpacking

(;α, δ, s) = m

(α = 0.3, β = 0.97, γ = 4.0, δ = 0.1, s = 0.2)

Functions

#matlab-like

function  fun(a,b)
    x = (a+b)
    return x
end

function  fun(a)
    return fun(a,a)
end

# you can specialize based on argument types
# multiple dispatch
function  fun(a,b::String)
    if b=="double"
        return a*2
    elseif b=="triple"
        return a*3
    else
        throw(error("Unkonwn string"))
    end
end

fun (generic function with 3 methods)

fun([1,2], [3,4])

2-element Vector{Int64}:
 4
 6

fun(1,"hundred")

ErrorException: Unkonwn string
Unkonwn string



Stacktrace:

 [1] error(s::String)

   @ Base ./error.jl:44

 [2] fun(a::Int64, b::String)

   @ Main ~/Teaching/econobits/eco309/corrections/jl_notebook_cell_df34fa98e69747e1a8f8a730347b8e2f_X52sZmlsZQ==.jl:19

 [3] top-level scope

   @ ~/Teaching/econobits/eco309/corrections/jl_notebook_cell_df34fa98e69747e1a8f8a730347b8e2f_X53sZmlsZQ==.jl:1

function fun2(a,b; l=1.0)
    return a+b*l
end

fun2 (generic function with 1 method)

fun2(1,3; l=2)

# one liners (equivalent but shorter)
fun3(a,b;l=1.0) = a+b*l

fun3 (generic function with 1 method)

# anonymous 

(a,b)->a^b

#65 (generic function with 1 method)

((a,b)->a^b)(2.0, 2.0)

4.0

maximum(u->u^2, 1:10)

control flow

for el ∈ 1:10 # all values from 1 to 10 included
end

v = [3.0]

1-element Vector{Float64}:
 3.0

# grow a vector with push!
push!(v, 4.0)

2-element Vector{Float64}:
 3.0
 4.0