reorganize chapters
This commit is contained in:
Bogumił Kamiński
475
ch03.jl
475
ch03.jl
@@ -2,358 +2,141 @@
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# Codes for chapter 3
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# Code for listing 3.1
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# Code from section 3.1
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aq = [10.0 8.04 10.0 9.14 10.0 7.46 8.0 6.58
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8.0 6.95 8.0 8.14 8.0 6.77 8.0 5.76
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13.0 7.58 13.0 8.74 13.0 12.74 8.0 7.71
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9.0 8.81 9.0 8.77 9.0 7.11 8.0 8.84
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11.0 8.33 11.0 9.26 11.0 7.81 8.0 8.47
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14.0 9.96 14.0 8.1 14.0 8.84 8.0 7.04
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6.0 7.24 6.0 6.13 6.0 6.08 8.0 5.25
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4.0 4.26 4.0 3.1 4.0 5.39 19.0 12.50
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12.0 10.84 12.0 9.13 12.0 8.15 8.0 5.56
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7.0 4.82 7.0 7.26 7.0 6.42 8.0 7.91
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5.0 5.68 5.0 4.74 5.0 5.73 8.0 6.89]
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methods(cd)
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# Code for checking size of a matrix
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sum isa Function
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size(aq)
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size(aq, 1)
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size(aq, 2)
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typeof(sum)
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typeof(sum) == Function
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# Code comparing tuple to a vector
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supertype(typeof(sum))
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v = [1, 2, 3]
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t = (1, 2, 3)
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v[1]
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t[1]
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v[1] = 10
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v
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t[1] = 10
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function traverse(T)
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println(T)
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T == Any || traverse(supertype(T))
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return nothing
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end
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traverse(Int64)
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# Code for figure 3.2
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function print_subtypes(T, indent_level=0)
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println(" " ^ indent_level, T)
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for S in subtypes(T)
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print_subtypes(S, indent_level + 2)
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end
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return nothing
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end
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print_subtypes(Integer)
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traverse(typeof([1.0, 2.0, 3.0]))
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traverse(typeof(1:3))
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AbstractVector
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typejoin(typeof([1.0, 2.0, 3.0]), typeof(1:3))
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# Code from section 3.2
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fun(x) = println("unsupported type")
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fun(x::Number) = println("a number was passed")
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fun(x::Float64) = println("a Float64 value")
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methods(fun)
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fun("hello!")
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fun(1)
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fun(1.0)
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bar(x, y) = "no numbers passed"
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bar(x::Number, y) = "first argument is a number"
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bar(x, y::Number) = "second argument is a number"
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bar("hello", "world")
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bar(1, "world")
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bar("hello", 2)
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bar(1, 2)
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bar(x::Number, y::Number) = "both arguments are numbers"
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bar(1, 2)
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methods(bar)
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function winsorized_mean(x::AbstractVector, k::Integer)
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k >= 0 || throw(ArgumentError("k must be non-negative"))
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length(x) > 2 * k || throw(ArgumentError("k is too large"))
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y = sort!(collect(x))
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for i in 1:k
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y[i] = y[k + 1]
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y[end - i + 1] = y[end - k]
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end
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return sum(y) / length(y)
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end
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winsorized_mean([8, 3, 1, 5, 7], 1)
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winsorized_mean(1:10, 2)
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winsorized_mean(1:10, "a")
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winsorized_mean(10, 1)
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winsorized_mean(1:10, -1)
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winsorized_mean(1:10, 5)
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# Code from section 3.3
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module ExampleModule
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function example()
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println("Hello")
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end
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end # ExampleModule
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import Statistics
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x = [1, 2, 3]
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mean(x)
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Statistics.mean(x)
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using Statistics
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mean(x)
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# start a fresh Julia session before running this code
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mean = 1
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using Statistics
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mean
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# start a fresh Julia session before running this code
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using Statistics
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mean([1, 2, 3])
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mean = 1
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# start a fresh Julia session before running this code
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using Statistics
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mean = 1
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mean([1, 2, 3])
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# start a fresh Julia session before running this code
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using Statistics
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using StatsBase
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?winsor
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mean(winsor([8, 3, 1, 5, 7], count=1))
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# Code from section 3.4
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@time 1 + 2
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@time(1 + 2)
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@assert 1 == 2 "1 is not equal 2"
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@assert(1 == 2, "1 is not equal 2")
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@macroexpand @assert(1 == 2, "1 is not equal 2")
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@macroexpand @time 1 + 2
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# before running these codes
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# define the winsorized_mean function using the code from section 3.1
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using BenchmarkTools
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@benchmark (1, 2, 3)
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@benchmark [1, 2, 3]
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x = rand(10^6);
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@benchmark winsorized_mean($x, 10^5)
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using Statistics, StatsBase
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@benchmark mean(winsor($x; count=10^5))
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# Code for section 3.1.2
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using Statistics
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mean(aq; dims=1)
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std(aq; dims=1)
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map(mean, eachcol(aq))
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map(std, eachcol(aq))
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map(eachcol(aq)) do col
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mean(col)
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end
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[mean(col) for col in eachcol(aq)]
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[std(col) for col in eachcol(aq)]
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# Code for section 3.1.3
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[mean(aq[:, j]) for j in axes(aq, 2)]
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[std(aq[:, j]) for j in axes(aq, 2)]
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axes(aq, 2)
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?Base.OneTo
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[mean(view(aq, :, j)) for j in axes(aq, 2)]
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[std(@view aq[:, j]) for j in axes(aq, 2)]
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# Code for section 3.1.4
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using BenchmarkTools
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x = ones(10^7, 10)
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@benchmark [mean(@view $x[:, j]) for j in axes($x, 2)]
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@benchmark [mean($x[:, j]) for j in axes($x, 2)]
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@benchmark mean($x, dims=1)
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# Code for section 3.1.5
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[cor(aq[:, i], aq[:, i+1]) for i in 1:2:7]
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collect(1:2:7)
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# Code for section 3.1.6
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y = aq[:, 2]
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X = [ones(11) aq[:, 1]]
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X \ y
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[[ones(11) aq[:, i]] \ aq[:, i+1] for i in 1:2:7]
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function R²(x, y)
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X = [ones(11) x]
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model = X \ y
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prediction = X * model
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error = y - prediction
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SS_res = sum(v -> v ^ 2, error)
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mean_y = mean(y)
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SS_tot = sum(v -> (v - mean_y) ^ 2, y)
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return 1 - SS_res / SS_tot
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end
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[R²(aq[:, i], aq[:, i+1]) for i in 1:2:7]
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?²
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# Code for section 3.1.7
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using Plots
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scatter(aq[:, 1], aq[:, 2]; legend=false)
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plot(scatter(aq[:, 1], aq[:, 2]; legend=false),
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scatter(aq[:, 3], aq[:, 4]; legend=false),
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scatter(aq[:, 5], aq[:, 6]; legend=false),
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scatter(aq[:, 7], aq[:, 8]; legend=false))
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plot([scatter(aq[:, i], aq[:, i+1]; legend=false)
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for i in 1:2:7]...)
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# Code for section 3.2
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two_standard = Dict{Int, Int}()
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for i in [1, 2, 3, 4, 5, 6]
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for j in [1, 2, 3, 4, 5, 6]
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s = i + j
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if haskey(two_standard, s)
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two_standard[s] += 1
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else
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two_standard[s] = 1
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end
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end
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end
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two_standard
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keys(two_standard)
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values(two_standard)
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using Plots
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scatter(collect(keys(two_standard)), collect(values(two_standard));
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legend=false, xaxis=2:12)
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all_dice = [[1, x2, x3, x4, x5, x6]
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for x2 in 2:11
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for x3 in x2:11
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for x4 in x3:11
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for x5 in x4:11
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for x6 in x5:11]
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for d1 in all_dice, d2 in all_dice
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test = Dict{Int, Int}()
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for i in d1, j in d2
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s = i + j
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if haskey(test, s)
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test[s] += 1
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else
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test[s] = 1
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end
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end
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if test == two_standard
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println(d1, " ", d2)
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end
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end
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# Code for section 3.3
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aq = [10.0 8.04 10.0 9.14 10.0 7.46 8.0 6.58
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8.0 6.95 8.0 8.14 8.0 6.77 8.0 5.76
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13.0 7.58 13.0 8.74 13.0 12.74 8.0 7.71
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9.0 8.81 9.0 8.77 9.0 7.11 8.0 8.84
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11.0 8.33 11.0 9.26 11.0 7.81 8.0 8.47
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14.0 9.96 14.0 8.1 14.0 8.84 8.0 7.04
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6.0 7.24 6.0 6.13 6.0 6.08 8.0 5.25
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4.0 4.26 4.0 3.1 4.0 5.39 19.0 12.50
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12.0 10.84 12.0 9.13 12.0 8.15 8.0 5.56
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7.0 4.82 7.0 7.26 7.0 6.42 8.0 7.91
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5.0 5.68 5.0 4.74 5.0 5.73 8.0 6.89]
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dataset1 = (x=aq[:, 1], y=aq[:, 2])
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dataset1[1]
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dataset1.x
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# Code for listing 3.2
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data = (set1=(x=aq[:, 1], y=aq[:, 2]),
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set2=(x=aq[:, 3], y=aq[:, 4]),
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set3=(x=aq[:, 5], y=aq[:, 6]),
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set4=(x=aq[:, 7], y=aq[:, 8]))
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# Code for section 3.3.2
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using Statistics
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map(s -> mean(s.x), data)
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map(s -> cor(s.x, s.y), data)
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using GLM
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model = lm(@formula(y ~ x), data.set1)
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r2(model)
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# Code for section 3.3.3
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model.mm
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x = [3, 1, 2]
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sort(x)
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x
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sort!(x)
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x
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empty_field!(nt, i) = empty!(nt[i])
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nt = (dict = Dict("a" => 1, "b" => 2), int=10)
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empty_field!(nt, 1)
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nt
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# Code for section 3.4.1
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x = [1 2 3]
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y = [1, 2, 3]
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x * y
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a = [1, 2, 3]
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b = [4, 5, 6]
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a * b
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a .* b
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map(*, a, b)
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[a[i] * b[i] for i in eachindex(a, b)]
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eachindex(a, b)
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eachindex([1, 2, 3], [4, 5])
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map(*, [1, 2, 3], [4, 5])
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[1, 2, 3] .* [4, 5]
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# Code for section 3.4.2
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[1, 2, 3] .* [4]
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[1, 2, 3] .^ 2
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[1, 2, 3, 4, 5, 6, 7, 8, 9, 10] .* [1 2 3 4 5 6 7 8 9 10]
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["x", "y", "z"] .=> [sum minimum maximum]
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abs.([1, -2, 3, -4])
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abs([1, 2, 3])
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string(1, 2, 3)
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string.("x", 1:10)
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f(i::Int) = string("got integer ", i)
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f(s::String) = string("got string ", s)
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f.([1, "1"])
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# Code for section 3.4.3
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in(1, [1, 2, 3])
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in(4, [1, 2, 3])
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in([1, 3, 5, 7, 9], [1, 2, 3, 4])
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in.([1, 3, 5, 7, 9], [1, 2, 3, 4])
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in.([1, 3, 5, 7, 9], Ref([1, 2, 3, 4]))
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# Code for section 3.4.4
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aq = [10.0 8.04 10.0 9.14 10.0 7.46 8.0 6.58
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8.0 6.95 8.0 8.14 8.0 6.77 8.0 5.76
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13.0 7.58 13.0 8.74 13.0 12.74 8.0 7.71
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9.0 8.81 9.0 8.77 9.0 7.11 8.0 8.84
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11.0 8.33 11.0 9.26 11.0 7.81 8.0 8.47
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14.0 9.96 14.0 8.1 14.0 8.84 8.0 7.04
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6.0 7.24 6.0 6.13 6.0 6.08 8.0 5.25
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4.0 4.26 4.0 3.1 4.0 5.39 19.0 12.50
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12.0 10.84 12.0 9.13 12.0 8.15 8.0 5.56
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7.0 4.82 7.0 7.26 7.0 6.42 8.0 7.91
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5.0 5.68 5.0 4.74 5.0 5.73 8.0 6.89]
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using Statistics
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mean.(eachcol(aq))
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mean(eachcol(aq))
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function R²(x, y)
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X = [ones(11) x]
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model = X \ y
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prediction = X * model
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error = y - prediction
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SS_res = sum(v -> v ^ 2, error)
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mean_y = mean(y)
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SS_tot = sum(v -> (v - mean_y) ^ 2, y)
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return 1 - SS_res / SS_tot
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end
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function R²(x, y)
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X = [ones(11) x]
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model = X \ y
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prediction = X * model
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SS_res = sum((y .- prediction) .^ 2)
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SS_tot = sum((y .- mean(y)) .^ 2)
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return 1 - SS_res / SS_tot
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end
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# Code for section 3.5
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[]
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Dict()
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Float64[1, 2, 3]
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Dict{UInt8, Float64}(0 => 0, 1 => 1)
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UInt32(200)
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Real[1, 1.0, 0x3]
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v1 = Any[1, 2, 3]
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eltype(v1)
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v2 = Float64[1, 2, 3]
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eltype(v2)
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v3 = [1, 2, 3]
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eltype(v2)
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d1 = Dict()
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eltype(d1)
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d2 = Dict(1 => 2, 3 => 4)
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eltype(d2)
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p = 1 => 2
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typeof(p)
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# Code for section 3.5.1
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[1, 2, 3] isa AbstractVector{Int}
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[1, 2, 3] isa AbstractVector{Real}
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AbstractVector{<:Real}
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# Code for section 3.5.2
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using Statistics
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function ourcov(x::AbstractVector{<:Real},
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y::AbstractVector{<:Real})
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len = length(x)
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@assert len == length(y) > 0
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return sum((x .- mean(x)) .* (y .- mean(y))) / (len - 1)
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end
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ourcov(1:4, [1.0, 3.0, 2.0, 4.0])
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cov(1:4, [1.0, 3.0, 2.0, 4.0])
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ourcov(1:4, Any[1.0, 3.0, 2.0, 4.0])
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x = Any[1, 2, 3]
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identity.(x)
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y = Any[1, 2.0]
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identity.(y)
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@edit winsor(x, count=10^5)
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