東吳大學分享

1. 當
遇上資料科學
Julia Taiwan發起人 杜岳華
1

2. 自我介紹
 杜岳華
 疾病管制署小小研發替代役
 想成為生醫資料科學家
 陽明生醫資訊所碩士
 成大醫學檢驗生物技術系學士
 成大資訊工程系學士
2

3. Why Julia?
3

4. In scientific computing and data science…
4

5. Other users
5

6. Avoid two language problem
 One language for rapid development
 The other for performance
 Example:
 Python for rapid development
 C for performance
6

7. itertools的效能
 一篇文章描述兩者的取捨
 「一般來說，我們不會去優化所有的程式碼，因為優化有很
大的代價:一般性與可讀性。 通常跑得快與寫的快，是要做
取捨的。 這裡的例子很好想像，大家只要比較R的程式碼與
Rcpp的程式碼就好了。」
http://wush.ghost.io/itertools-performance/
7

8. 使用Julia就不用做取捨了阿!!
8

9. Julia的特色
 Write like Python, run like C.
 擁有python的可讀性 (readibility)
 擁有C的效能
 Easy to parallelism
 內建套件管理器
 ……
9

10. Julia code
a = [1, 2, 3, 4, 5]
function square(x)
return x^2
end
for x in a
println(square(x))
end
10

11. https://julialang.org/benchmarks/
Julia performance
11

12. Who use Julia?
12

13.  Nobel prize in economic sciences
 The founder of QuantEcon
 “His team at NYU uses Julia for macroeconomic modeling and contributes
to the Julia ecosystem.”
https://juliacomputing.com/case-studies/thomas-sargent.html
13

14.  In 2015, economists at the Federal Reserve Bank of New York (FRBNY)
published FRBNY’s most comprehensive and complex macroeconomic
models, known as Dynamic Stochastic General Equilibrium, or DSGE
models, in Julia.
https://juliacomputing.com/case-studies/ny-fed.html
14

15.  UK cancer researchers turned to Julia to run simulations of tumor growth.
Nature Genetics, 2016
 Approximate Bayesian Computation (ABC) algorithms require potentially millions of
simulations - must be fast
 BioJulia project for analyzing biological data in Julia
 Bayesian MCMC methods Lora.jl and Mamba.jl
https://juliacomputing.com/case-studies/nature.html
15

16.  IBM and Julia Computing analyzed eye fundus images provided by Drishti
Eye Hospitals.
 Timely screening for changes in the retina can help get them to treatment
and prevent vision loss. Julia Computing’s work using deep learning
makes retinal screening an activity that can be performed by a trained
technician using a low cost fundus camera.
https://juliacomputing.com/case-studies/ibm.html
16

17.  Path BioAnalytics is a computational biotech company developing novel
precision medicine assays to support drug discovery and development,
and treatment of disease.
https://juliacomputing.com/case-studies/pathbio.html
17

18.  The Sloan Digital Sky Survey contains nearly 5 million telescopic images of
12 megabytes each – a dataset of 55 terabytes.
 In order to analyze this massive dataset, researchers at UC Berkeley and
Lawrence Berkeley National Laboratory created a new code named
Celeste.
https://juliacomputing.com/case-studies/intel-astro.html
18

19. http://pkg.julialang.org/pulse.html
Julia Package Ecosystem Pulse
19

20. Introduction to Julia
20

21. 一切都從數字開始…
 在Julia中數字有下列幾種形式
 整數
 浮點數
 有理數
 複數
21

22. Julia的整數跟浮點數是有不同位元版本的
Integer
Int8
Int16
Int32
Int64
Int128
Unsigned
Uint8
Uint16
Uint32
Uint64
Uint128
Float
Float16
Float32
Float64
22

23. 有理數
 有理數表示
 自動約分
 自動調整負號
 接受分母為0
2//3 # 2//3
-6//12 # -1//2
5//-20 # -1//4
5//0 # 1//0
num(2//10) # 1
den(7//14) # 2
2//4 + 1//7 # 9//14
3//10 * 6//9 # 1//5
10//15 == 8//12 # true
float(3//4) # 0.7523

24. 複數
1 + 2im
(1 + 2im) + (3 - 4im) # 4 - 2im
(1 + 2im)*(3 - 4im) # 11 + 2im
(-4 + 3im)^(2 + 1im) # 1.950 + 0.651im
real(1 + 2im) # 1
imag(3 + 4im) # 4
conj(1 + 2im) # 1 - 2im
abs(3 + 4im) # 5.0
angle(3 + 3im)/pi*180 # 45.0
24

25. 我們來宣告變數吧！
 指定或不指定型別
x = 5
y = 4::Int64
z = x + y
println(z) # 9
25

26. 變數可以很隨便
 動態型別語言特性
 Value is immutable
x = 5
println(x) # 5
println(typeof(x)) # Int64
x = 6.0
println(x) # 6.0
println(typeof(x)) # Float64
26

27. x
6.0
5
27

28. 靜態型別與動態型別
 靜態型別跟動態型別最大的差別在於型別是跟著變數還是值。
5
5
x
x
28

29. 躺著玩、坐著玩、趴著玩，還是運算子好
玩
 +x： 就是x本身
 -x： 變號
 x + y, x - y, x * y, x / y： 一般四則運算
 div(x, y)： 商
 x % y： 餘數，也可以用rem(x, y)
 x y： 反除，等價於y / x
 x ^ y： 次方
29

30. 操縱數字的機械核心
 ~x： bitwise not
 x & y： bitwise and
 x | y： bitwise or
 x $ y: bitwise xor
 x >>> y：無正負號，將x的位元右移y個位數
 x >> y：保留正負號，將x的位元右移y個位數
 x << y： 將x的位元左移y個位數
https://www.technologyuk.net/mathematics/number-systems/images/binary_number.gif
30

31. 方便的更新方法
 +=
 -=
 *=
 /=
 =
 %=
 ^=
 &=
 |=
 $=
 >>>=
 >>=
 <<=
x += 5
等價於
x = x + 5
31

32. 超級比一比
 x == y：等於
 x != y, x ≠ y：不等於
 x < y：小於
 x > y：大於
 x <= y, x ≤ y：小於或等於
 x >= y, x ≥ y：大於或等於
a, b, c = (1, 3, 5)
a < b < c # true
32

33. 不同型別的運算與轉換
 算術運算會自動轉換
 強型別
3.14 * 4 # 12.56
parse(“5”) # 5
convert(AbstractString, 5) # “5”
33

34. 強型別與弱型別
5 “5”
5 “5”
+
+
Implicitly
34

35. 感覺這樣有點乾
 我們來寫個小遊戲好了
35

36. 來寫個猜拳遊戲好了
paper = 1 # 這代表布
scissor = 2 # 這代表剪刀
stone = 3 # 這代表石頭
36

37. 判斷輸贏
 If判斷式
 短路邏輯
if scissor > paper
println("scissor win!!")
end
if <判斷式>
<程式碼>
end
if 3 > 5 && 10 > 0
…
end 37

38. 使用者輸入
println("請輸入要出的拳”)
println(“1代表布，2代表剪刀，3代表石頭：")
s = readline(STDIN)
x = parse(s)
38

39. 組織起來
if x == paper
println("你出布")
elseif x == scissor
println("你出剪刀")
elseif x == stone
println("你出石頭")
end
if <判斷式1>
<程式碼1>
elseif <判斷式2>
<程式碼2>
else
<程式碼3>
end
39

40. 電腦怎麼出拳
 rand(): 隨機0~1
 rand([]): 從裡面選一個出來
y = rand([1, 2, 3])
40

41. 巢狀比較
if x == y
println("平手")
elseif x == paper
println("你出布")
if y == scissor
println("電腦出剪刀")
println("電腦贏了")
elseif y == stone
println("電腦出石頭")
println("你贏了")
end
... 41

42. 我的義大利麵條
elseif x == scissor
println("你出剪刀")
if y == paper
println("電腦出布")
println("你贏了")
elseif y == stone
println("電腦出石頭")
println("電腦贏了")
endelseif x == stone
println("你出石頭")
if y == scissor
println("電腦出剪刀")
println("你贏了")
elseif y == paper
println("電腦出布")
println("電腦贏了")
end
end
if x == y
println("平手")
elseif x == paper
println("你出布")
if y == scissor
println("電腦出剪刀")
println("電腦贏了")
elseif y == stone
println("電腦出石頭")
println("你贏了")
end 42

43. 我看到重複了
 函式是消除重複的好工具！
 像我們之前有寫了非常多的條件判斷，其實重複性很高，感
覺很蠢，我們可以設法把出拳的判斷獨立出來。
43

44. 函式來幫忙
function add(a, b)
c = a + b
return c
end
44

45. 函式怎麼講話
 pass-by-sharing
 個人認為跟call by reference比較像就是了
5x
function foo(a)
end
a
45

46. 簡化重複
function shape(x)
if x == paper
return "布"
elseif x == scissor
return "剪刀"
elseif x == stone
return "石頭"
end
end
46

47. 要怎麼處理判定輸贏?
 簡化了重複
 可是沒有處理判定輸贏
47

48. 你需要的是一個矩陣
 突然神說了一句話，解救了凡人的我。XD
 是的，或許你需要一個表來讓你查。
| 布 剪刀 石頭
-------------------
布| 0 -1 1
剪刀| 1 0 -1
石頭| -1 1 0
48

49. 介紹Array
 homogenous
 start from 1
 mutable
[ ]2 3 5
A = [2, 3, 5]
A[2] # 3
49

50. 多維陣列
A = [0, -1, 1;
1, 0, -1;
-1, 1, 0]
A[1, 2]
50

51. 字串的簡易操作
 concatenate
 x要是字串
"你出" * x
51

52. 簡化完畢
 稱為重構
 refactoring
x_shape = shape(x)
y_shape = shape(y)
println("你出" * x_shape)
println("電腦出" * y_shape)
win_or_lose = A[x, y]
if win_or_lose == 0
println("平手")
elseif win_or_lose == 1
println("你贏了")
else
println("電腦贏了")
end
52

53. 我想玩很多次
while <判斷式>
<程式碼>
end
x = …
while <持續條件>
...
x = …
end
53

54. 停止條件
s = readline(STDIN)
x = parse(s)
while x != -1
...
s = readline(STDIN)
x = parse(s)
end
54

55. Julia其他常用語法
 For loop
 Comprehension
 Collections
55

56. For loop
for i = 1:5 # for迴圈，有限的迴圈次數
println(i)
end
56

57. Array搭配for loop
strings = ["foo","bar","baz"]
for s in strings
println(s)
end
57

58. 數值運算
 介紹各種Array函式
zeros(Float64, 2, 2) # 2-by-2 matrix with 0
ones(Float64, 3, 3) # 3-by-3 matrix with 1
trues(2, 2) # 2-by-2 matrix with true
eye(3) # 3-by-3 diagnal matrix
rand(2, 2) # 2-by-2 matrix with random number
58

59. Comprehension
[x for x = 1:3]
[x for x = 1:20 if x % 2 == 0]
["$x * $y = $(x*y)" for x=1:9, y=1:9]
[1, 2, 3]
[2, 4, 6, 8, 10, 12, 14, 16, 18, 20]
[“1 * 1 = 1“, “1 * 2 = 2“, “1 * 3 = 3“ ...]
59

60. Tuple
 Immutable
tup = (1, 2, 3)
tup[1] # 1
tup[1:2] # (1, 2)
(a, b, c) = (1, 2, 3)
60

61. Set
 Mutable
filled = Set([1, 2, 2, 3, 4])
push!(filled, 5)
intersect(filled, other)
union(filled, other)
setdiff(Set([1, 2, 3, 4]), Set([2, 3, 5]))
Set([i for i=1:10])
61

62. Dict
 Mutable
filled = Dict("one"=> 1, "two"=> 2, "three"=> 3)
keys(filled)
values(filled)
Dict(x=> i for (i, x) in enumerate(["one", "two",
"three", "four"]))
62

63. Julia special features
63

64. 支援UTF8符號
 打`alpha<tab>` => α
 α = 1 # 作為變數名稱
 μ = 0
 σ = 1
 normal = Normal(μ, σ)
64

65. Easy to optimize
 Allow generalization and flexibility, and enable to optimize.
 Hints:
 Avoid global variables
 Add type declarations
 Measure performance with @time and pay attention to memory
allocation
 ……
65

66. Easy to profile
 Use @time
 ProfileView.view()
66

67. 增進MATLAB-style的程式效能
 有人在論壇上提到如何增進程式效能，作者發現原本的程式
碼約有50%的時間用在garbage collection，意味著有一半的
時間花在記憶體的分配及釋放
 作者進一步提到，以array-by-array的操作方式是在自
MATLAB背景的人會寫出的程式，若改成element-by-
element的方式就有大幅的改善
 P.S. 在v0.6之後加入了新的功能，不再讓cos(aEll).*gridX .-
sin(aEll).*gridY這樣的運算分配三次記憶體，而是只有一次
http://kristofferc.github.io/post/vectorization_performance_study/
67

68. Easy to parallelize
for i = 1:100000
do_something()
end
@parallel for i = 1:100000
do_something()
end
68

69. Package manager
julia> Pkg.update()
julia> Pkg.add(“Foo”)
julia> Pkg.rm(“Foo”)
69

70. @code_native
julia> @code_native add(1, 2)
.text
Filename: REPL[2]
pushq %rbp
movq %rsp, %rbp
Source line: 2
leaq (%rcx,%rdx), %rax
popq %rbp
retq
nopw (%rax,%rax)
function add(a, b)
return a+b
end
70

71. @code_llvm
julia> @code_llvm add(1, 2.0)
; Function Attrs: uwtable
define double @julia_add_71636(i64, double) #0 {
top:
%2 = sitofp i64 %0 to double
%3 = fadd double %2, %1
ret double %3
}
function add(a, b)
return a+b
end
71

72. Julia packages
72

73. 73

74. 74

75. 75

76. 76

77. 77

78. DataTables.jl
julia> using DataTables
julia> dt = DataTable(A = 1:4, B = ["M", "F", "F", "M"])
4×2 DataTables.DataTable
│ Row │ A │ B │
├─────┼───┼───┤
│ 1 │ 1 │ M │
│ 2 │ 2 │ F │
│ 3 │ 3 │ F │
│ 4 │ 4 │ M │
78

79. DataTables.jl
julia> dt[:A]
4-element NullableArrays.NullableArray{Int64,1}:
1
2
3
4
julia> dt[2, :A]
Nullable{Int64}(2)
79

80. DataTables.jl
julia> dt = readtable("data.csv")
julia> dt = DataTable(A = 1:10);
julia> writetable("output.csv", dt)
80

81. DataTables.jl
julia> names = DataTable(ID = [1, 2], Name = ["John
Doe", "Jane Doe"])
julia> jobs = DataTable(ID = [1, 2], Job = ["Lawyer",
"Doctor"])
julia> full = join(names, jobs, on = :ID)
2×3 DataTables.DataTable
│ Row │ ID │ Name │ Job │
├─────┼────┼──────────┼────────┤
│ 1 │ 1 │ John Doe │ Lawyer │
│ 2 │ 2 │ Jane Doe │ Doctor │ 81

82. Query.jl
julia> q1 = @from i in dt begin
@where i.age > 40
@select {number_of_children=i.children, i.name}
@collect DataTable
end
82

83. StatsBase.jl
 Mean Functions
 mean(x, w)
 geomean(x)
 harmmean(x)
 Scalar Statistics
 var(x, wv[; mean=...])
 std(x, wv[; mean=...])
 mean_and_var(x[, wv][, dim])
 mean_and_std(x[, wv][, dim])
 zscore(X, μ, σ)
 entropy(p)
 crossentropy(p, q)
 kldivergence(p, q)
 percentile(x, p)
 nquantile(x, n)
 quantile(x)
 median(x, w)
 mode(x)
83

84. StatsBase.jl
 Sampling from Population
 sample(a)
 Correlation Analysis of Signals
 autocov(x, lags[; demean=true])
 autocor(x, lags[; demean=true])
 corspearman(x, y)
 corkendall(x, y)
84

85. Distributions.jl
 Continuous Distributions
 Beta(α, β)
 Chisq(ν)
 Exponential(θ)
 Gamma(α, θ)
 LogNormal(μ, σ)
 Normal(μ, σ)
 Uniform(a, b)
 Discrete Distributions
 Bernoulli(p)
 Binomial(n, p)
 DiscreteUniform(a, b)
 Geometric(p)
 Hypergeometric(s, f, n)
 NegativeBinomial(r, p)
 Poisson(λ)
85

86. GLM.jl
86
julia> data = DataFrame(X=[1,2,3], Y=[2,4,7])
3x2 DataFrame
|-------|---|---|
| Row # | X | Y |
| 1 | 1 | 2 |
| 2 | 2 | 4 |
| 3 | 3 | 7 |

87. GLM.jl
87
julia> OLS = glm(@formula(Y ~ X), data, Normal(),
IdentityLink())
DataFrameRegressionModel{GeneralizedLinearModel,Float64
}:
Coefficients:
Estimate Std.Error z value Pr(>|z|)
(Intercept) -0.666667 0.62361 -1.06904 0.2850
X 2.5 0.288675 8.66025 <1e-17

88. GLM.jl
88
julia> newX = DataFrame(X=[2,3,4]);
julia> predict(OLS, newX, :confint)
3×3 Array{Float64,2}:
4.33333 1.33845 7.32821
6.83333 2.09801 11.5687
9.33333 1.40962 17.257
# The columns of the matrix are prediction, 95% lower
and upper confidence bounds

89. Gadfly.jl
89

90. Plots.jl
90
# initialize the attractor
n = 1500
dt = 0.02
σ, ρ, β = 10., 28., 8/3
x, y, z = 1., 1., 1.
# initialize a 3D plot with 1 empty series
plt = path3d(1, xlim=(-25,25), ylim=(-25,25), zlim=(0,50), xlab =
"x", ylab = "y", zlab = "z", title = "Lorenz Attractor", marker = 1)
# build an animated gif, saving every 10th frame
@gif for i=1:n
dx = σ*(y - x) ; x += dt * dx
dy = x*(ρ - z) - y ; y += dt * dy
dz = x*y - β*z ; z += dt * dz
push!(plt, x, y, z)
end every 10

91. Data
 JuliaData
 DataTables.jl
 CSV.jl
 DataStreams.jl
 CategoricalArrays.jl
 JuliaDB
91

92. File
 JuliaIO
 FileIO.jl
 JSON.jl
 LightXML.jl
 HDF5.jl
 GZip.jl
92

93. Differential equation
 JuliaDiff
 ForwardDiff.jl: Forward Mode Automatic Differentiation for Julia
 ReverseDiff.jl: Reverse Mode Automatic Differentiation for Julia
 TaylorSeries.jl
 JuliaDiffEq
 DifferentialEquations.jl
 Discrete Equations (function maps, discrete stochastic (Gillespie/Markov) simulations)
 Ordinary Differential Equations (ODEs)
 Stochastic Differential Equations (SDEs)
 Algebraic Differential Equations (DAEs)
 Delay Differential Equations (DDEs)
 (Stochastic) Partial Differential Equations ((S)PDEs) 93

94. Probability
 JuliaStats
 JuliaOpt
 JuMP.jl
 Convex.jl
 JuliaML
 LearnBase.jl
 LossFunctions.jl
 ObjectiveFunctions.jl
 PenaltyFunctions.jl
 Klara.jl: MCMC inference in Julia
 Mamba.jl: Markov chain Monte
Carlo (MCMC) for Bayesian
analysis in julia
94

95. Graph / Network
 JuliaGraphs
 LightGraphs.jl
 GraphPlot.jl
95

96. Plot
 Gadfly.jl
 JuliaPlots
 Plots.jl
96

97. Glue
 JuliaPy
 PyCall.jl
 pyjulia
 Conda.jl
 PyPlot.jl
 Pandas.jl
 Seaborn.jl
 SymPy.jl
 JuliaInterop
 RCall.jl
 JavaCall.jl
 CxxWrap.jl
 MATLAB.jl
97

98. Programming
 JuliaCollections
 Iterators.jl
 DataStructures.jl
 SortingAlgorithms.jl
 FunctionalCollections.jl
 Combinatorics.jl
98

99. Web
 JuliaWeb
 Requests.jl
 HttpServer.jl
 WebSockets.jl
 HTTPClient.jl
99

100. 跟其他語言的比較
 Python
 R
 Perl
100

101. Jobs
 Apple, Amazon, Facebook, BlackRock, Ford, Oracle
 Comcast, Massachusetts General Hospital
 Farmers Insurance
 Los Alamos National Laboratory and the National
Renewable Energy Laboratory
101
https://juliacomputing.com/press/2017/01/18/jobs.html

102. Julia Taiwan
 FB社群:
https://www.facebook.com/groups/1787971081482186/
102