update chapters 4 and 5
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Bogumił Kamiński
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ch04.jl
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210
ch04.jl
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# Bogumił Kamiński, 2021
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# Codes for chapter 4
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# Code for listing 4.1
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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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# Code for checking size of a matrix
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size(aq)
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size(aq, 1)
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size(aq, 2)
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# Code comparing tuple to a vector
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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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# Code for figure 4.2
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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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# Code for section 4.1.2
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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 4.1.3
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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 4.1.4
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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 4.1.5
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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 4.1.6
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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 4.1.7
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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 4.2
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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 4.3
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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 4.2
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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 4.3.2
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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 4.3.3
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model.mm
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x = [3, 1, 3, 2]
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unique(x)
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x
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unique!(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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