Codes for chapters 1, 2, and 3

ch02.jl

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+# Bogumił Kamiński, 2021
+
+# Codes for chapter 2
+
+# Code for listing 2.1
+
+1
+true
+"Hello world!"
+0.1
+[1, 2, 3]
+
+# Code for listing 2.2
+
+typeof(1)
+typeof(true)
+typeof("Hello world!")
+typeof(0.1)
+typeof([1, 2, 3])
+
+# Code for showing bit representation of numbers
+
+bitstring(1)
+bitstring(1.0)
+bitstring(Int8(1))
+
+# Code showing to what Int alias expands
+
+Int
+
+# Code for checking if value is of some type
+
+[1, 2, 3] isa Vector{Int}
+[1, 2, 3] isa Array{Int64, 1}
+
+# Code for section 2.2
+
+x = 1
+y = [1, 2, 3]
+
+x = 1
+x
+typeof(x)
+x = 0.1
+x
+typeof(x)
+
+Kamiński = 1
+x₁ = 0.5
+ε = 0.0001
+
+?₁
+?ε
+
+# Code for listing 2.3
+
+x = -7
+if x > 0
+    println("positive")
+elseif x < 0
+    println("negative")
+elseif x == 0
+    println("zero")
+else
+    println("unexpected condition")
+end
+
+# Code showing that logical condition must be Bool
+
+x = -7
+if x
+    println("condition was true")
+end
+
+# Code showing comparisons against NaN
+
+NaN > 0
+NaN >= 0
+NaN < 0
+NaN <= 0
+NaN == 0
+
+NaN != 0
+NaN != NaN
+
+# Code showing that floating point arithmetic is only approximate
+
+0.1 + 0.2 == 0.3
+
+0.1 + 0.2
+
+isapprox(0.1 + 0.2, 0.3)
+
+0.1 + 0.2 ≈ 0.3
+
+# Code showing combining conditions
+
+x = -7
+x > 0 && x < 10
+x < 0 || log(x) > 10
+
+x = -7
+log(x)
+
+# Code showing typical one-line conditional execution expressions
+
+x = -7
+x < 0 && println(x^2)
+iseven(x) || println("x is odd")
+
+x = -7
+if x < 0
+    println(x^2)
+end
+if !iseven(x)
+    println("x is odd")
+end
+
+x = -7
+if x < 0 && x^2
+    println("inside if")
+end
+
+# Code showing ternary operator
+
+x = -7
+x > 0 ? println("x is positive") : println("x is not positive")
+
+# Code from listing 2.4
+
+for i in [1, 2, 3]
+    println(i, " is ", isodd(i) ? "odd" : "even")
+end
+
+# Code from listing 2.5
+
+i = 1
+while i < 4
+    println(i, " is ", isodd(i) ? "odd" : "even")
+    global i += 1
+end
+
+# Code showing break and continue keywords
+
+i = 0
+while true
+    global i += 1
+    i > 6 && break
+    isodd(i) && continue
+    println(i, " is even")
+end
+
+# Code from listing 2.6
+
+x = -7
+x < 0 && begin
+    println(x)
+    x += 1
+    println(x)
+    2 * x
+end
+x > 0 ? (println(x); x) : (x += 1; println(x); x)
+
+# Code from section 2.3.4
+
+x = [8, 3, 1, 5, 7]
+k = 1
+
+y = sort(x)
+
+for i in 1:k
+    y[i] = y[k + 1]
+    y[end - i + 1] = y[end - k]
+end
+y
+
+s = 0
+for v in y
+    s += v
+end
+s
+s / length(y)
+
+# Code from listing 2.7
+
+function times_two(x)
+    return 2 * x
+end
+times_two(10)
+
+# Code from listing 2.8
+
+function compose(x, y=10; a, b=10)
+    return x, y, a, b
+end
+compose(1, 2; a=3, b=4)
+compose(1, 2; a=3)
+compose(1; a=3)
+compose(1)
+compose(; a=3)
+
+# Code from listing 2.9
+
+times_two(x) = 2 * x
+compose(x, y=10; a, b=10) = x, y, a, b
+
+# Code showing the use of map function
+
+map(times_two, [1, 2, 3])
+
+# Code from listing 2.10
+
+map(x -> 2 * x, [1, 2, 3])
+
+# Code showing sum taking a function as a first argument
+
+sum(x -> x ^ 2, [1, 2, 3])
+
+# Code showing do-end syntax
+
+sum([1, 2, 3]) do x
+    println("processing ", x)
+    return x ^ 2
+end
+
+# Code showing the difference between sort and sort!
+
+x = [5, 1, 3, 2]
+sort(x)
+x
+sort!(x)
+x
+
+# Code showing a simple implementation of winsorized_mean function
+
+function winsorized_mean(x, k)
+    y = sort(x)
+    for i in 1:k
+        y[i] = y[k + 1]
+        y[end - i + 1] = y[end - k]
+    end
+    s = 0
+    for v in y
+        s += v
+    end
+    return s / length(y)
+end
+winsorized_mean([8, 3, 1, 5, 7], 1)
+
+# Code from section 2.5
+
+function fun1()
+    x = 1
+    return x + 1
+end
+fun1()
+x
+
+function fun2()
+    if true
+        x = 10
+    end
+    return x
+end
+fun2()
+
+function fun3()
+    x = 0
+    for i in [1, 2, 3]
+        if i == 2
+            x = 2
+        end
+    end
+    return x
+end
+fun3()
+
+function fun4()
+    for i in [1, 2, 3]
+        if i == 2
+            x = 2
+        end
+    end
+    return x
+end
+fun4()
+
+function fun5()
+    for i in [1, 2, 3]
+        if i == 1
+            x = 1
+        else
+            x += 1
+        end
+        println(x)
+    end
+end
+fun5()
+
+function fun6()
+    x = 0
+    for i in [1, 2, 3]
+        if i == 1
+            x = 1
+        else
+            x += 1
+        end
+        println(x)
+    end
+end
+fun6()
+
+# Code from section 2.6
+
+methods(cd)
+
+sum isa Function
+
+typeof(sum)
+typeof(sum) == Function
+
+supertype(typeof(sum))
+
+function traverse(T)
+    println(T)
+    T == Any || traverse(supertype(T))
+    return nothing
+end
+traverse(Int64)
+
+function print_subtypes(T, indent_level=0)
+    println(" " ^ indent_level, T)
+    for S in subtypes(T)
+        print_subtypes(S, indent_level + 2)
+    end
+    return nothing
+end
+print_subtypes(Integer)
+
+traverse(typeof([1.0, 2.0, 3.0]))
+traverse(typeof(1:3))
+
+AbstractVector
+
+typejoin(typeof([1.0, 2.0, 3.0]), typeof(1:3))
+
+# Code from section 2.7
+
+fun(x) = println("unsupported type")
+fun(x::Number) = println("a number was passed")
+fun(x::Float64) = println("a Float64 value")
+methods(fun)
+
+fun("hello!")
+fun(1)
+fun(1.0)
+
+bar(x, y) = "no numbers passed"
+bar(x::Number, y) = "first argument is a number"
+bar(x, y::Number) = "second argument is a number"
+bar("hello", "world")
+bar(1, "world")
+bar("hello", 2)
+bar(1, 2)
+
+bar(x::Number, y::Number) = "both arguments are numbers"
+bar(1, 2)
+methods(bar)
+
+function winsorized_mean(x::AbstractVector, k::Integer)
+    k >= 0 || throw(ArgumentError("k must be non-negative"))
+    length(x) > 2 * k || throw(ArgumentError("k is too large"))
+    y = sort!(collect(x))
+    for i in 1:k
+        y[i] = y[k + 1]
+        y[end - i + 1] = y[end - k]
+    end
+    return sum(y) / length(y)
+end
+
+winsorized_mean([8, 3, 1, 5, 7], 1)
+winsorized_mean(1:10, 2)
+winsorized_mean(1:10, "a")
+winsorized_mean(10, 1)
+
+winsorized_mean(1:10, -1)
+winsorized_mean(1:10, 5)
+
+# Code from section 2.8
+
+import Statistics
+x = [1, 2, 3]
+mean(x)
+Statistics.mean(x)
+
+using Statistics
+mean(x)
+
+# start a fresh Julia session before running this code
+mean = 1
+using Statistics
+mean
+
+# start a fresh Julia session before running this code
+using Statistics
+mean([1, 2, 3])
+mean = 1
+
+# start a fresh Julia session before running this code
+using Statistics
+mean = 1
+mean([1, 2, 3])
+
+# start a fresh Julia session before running this code
+using Statistics
+using StatsBase
+?winsor
+mean(winsor([8, 3, 1, 5, 7], count=1))
+
+# Code from section 2.9
+
+@time 1 + 2
+
+@time(1 + 2)
+
+@assert 1 == 2 "1 is not equal 2"
+@assert(1 == 2, "1 is not equal 2")
+
+@macroexpand @assert(1 == 2, "1 is not equal 2")
+
+@macroexpand @time 1 + 2
+
+# before running these codes
+# define the winsorized_mean function using the code from section 2.7
+
+using BenchmarkTools
+x = rand(10^6);
+@benchmark winsorized_mean($x, 10^5)
+using Statistics, StatsBase
+@benchmark mean(winsor($x; count=10^5))
+
+@edit winsor(x, count=10^5)