Introduction to Julia
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This document introduces Julia and provides an overview of its key features. It begins with introductions and background on why Julia was created. It then covers basic Julia concepts like variables, arithmetic operators, control flow, arrays, functions, and parallelization capabilities. The document also discusses Julia's built-in package ecosystem and provides examples of packages like DataFrames. It aims to provide attendees with foundational knowledge of the Julia programming language.
![Julia code
a = [1, 2, 3, 4, 5]
function square(x)
return x^2
end
for x in a
println(square(x))
end
10](https://image.slidesharecdn.com/20180610introductiontojulia-180610151833/85/Introduction-to-Julia-10-320.jpg)
![Array 搭配 for loop
strings = ["foo","bar","baz"]
for s in strings
println(s)
end
33](https://image.slidesharecdn.com/20180610introductiontojulia-180610151833/85/Introduction-to-Julia-33-320.jpg)
![Rand()
rand(): 隨機0~1
rand([]): 從裡面選一個出來
y = rand([1, 2, 3])
34](https://image.slidesharecdn.com/20180610introductiontojulia-180610151833/85/Introduction-to-Julia-34-320.jpg)
![Array
homogenous
start from 1
mutable
[ ]2 3 5
A = [2, 3, 5]
A[2] # 3
35](https://image.slidesharecdn.com/20180610introductiontojulia-180610151833/85/Introduction-to-Julia-35-320.jpg)
![多維陣列
A = [0 -1 1;
1 0 -1;
-1 1 0]
A[1, 2]
36](https://image.slidesharecdn.com/20180610introductiontojulia-180610151833/85/Introduction-to-Julia-36-320.jpg)
![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“ ...]
40](https://image.slidesharecdn.com/20180610introductiontojulia-180610151833/85/Introduction-to-Julia-40-320.jpg)
![Tuple
Immutable
tup = (1, 2, 3)
tup[1] # 1
tup[1:2] # (1, 2)
(a, b, c) = (1, 2, 3)
41](https://image.slidesharecdn.com/20180610introductiontojulia-180610151833/85/Introduction-to-Julia-41-320.jpg)
![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])
42](https://image.slidesharecdn.com/20180610introductiontojulia-180610151833/85/Introduction-to-Julia-42-320.jpg)
![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"]))
43](https://image.slidesharecdn.com/20180610introductiontojulia-180610151833/85/Introduction-to-Julia-43-320.jpg)
![@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
51](https://image.slidesharecdn.com/20180610introductiontojulia-180610151833/85/Introduction-to-Julia-51-320.jpg)
![DataFrames.jl
julia> using DataFrames
julia> df = DataFrame(A = 1:4, B = ["M", "F", "F", "M"])
4×2 DataFrames.DataFrame
│ Row │ A │ B │
├─────┼───┼───┤
│ 1 │ 1 │ M │
│ 2 │ 2 │ F │
│ 3 │ 3 │ F │
│ 4 │ 4 │ M │
59](https://image.slidesharecdn.com/20180610introductiontojulia-180610151833/85/Introduction-to-Julia-59-320.jpg)
![DataFrames.jl
julia> df[:A]
4-element NullableArrays.NullableArray{Int64,1}:
1
2
3
4
julia> df[2, :A]
Nullable{Int64}(2)
60](https://image.slidesharecdn.com/20180610introductiontojulia-180610151833/85/Introduction-to-Julia-60-320.jpg)
![DataFrames.jl
julia> names = DataFrame(ID = [1, 2], Name = ["John
Doe", "Jane Doe"])
julia> jobs = DataFrame(ID = [1, 2], Job = ["Lawyer",
"Doctor"])
julia> full = join(names, jobs, on = :ID)
2×3 DataFrames.DataFrame
│ Row │ ID │ Name │ Job │
├─────┼────┼──────────┼────────┤
│ 1 │ 1 │ John Doe │ Lawyer │
│ 2 │ 2 │ Jane Doe │ Doctor │ 62](https://image.slidesharecdn.com/20180610introductiontojulia-180610151833/85/Introduction-to-Julia-62-320.jpg)
![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)
64](https://image.slidesharecdn.com/20180610introductiontojulia-180610151833/85/Introduction-to-Julia-64-320.jpg)
![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)
65](https://image.slidesharecdn.com/20180610introductiontojulia-180610151833/85/Introduction-to-Julia-65-320.jpg)
![GLM.jl
67
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 |](https://image.slidesharecdn.com/20180610introductiontojulia-180610151833/85/Introduction-to-Julia-67-320.jpg)
![GLM.jl
69
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](https://image.slidesharecdn.com/20180610introductiontojulia-180610151833/85/Introduction-to-Julia-69-320.jpg)
Introduction to Julia
- 1. Introduction to 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
- 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
- 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
- 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
- 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 Integer Int8 Int16 Int32 Int64 Int128 Unsigned Uint8 Uint16 Uint32 Uint64 Uint128 Float Float16 Float32 Float64
- 22. 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) # 0.7522
- 23. 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 23
- 24. 變數 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 24
- 25. 算術運算子 +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 25
- 26. 位元運算子 ~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 26
- 27. 更新運算子 += -= *= /= = %= ^= &= |= $= >>>= >>= <<= x += 5 等價於 x = x + 5 27
- 28. 比較運算子 x == y：等於 x != y, x ≠ y：不等於 x < y：小於 x > y：大於 x <= y, x ≤ y：小於或等於 x >= y, x ≥ y：大於或等於 a, b, c = (1, 3, 5) a < b < c # true 28
- 29. 不同型別的運算與轉換 算術運算會自動轉換 強型別 3.14 * 4 # 12.56 parse(“5”) # 5 convert(AbstractString, 5) # “5” 29
- 30. If判斷式 短路邏輯 if <判斷式> <程式碼> end if 3 > 5 && 10 > 0 … end 30
- 31. While loop while <判斷式> <程式碼> end x = … while <持續條件> ... x = … end 31
- 32. For loop for i = 1:5 # for迴圈，有限的迴圈次數 println(i) end 32
- 33. Array 搭配 for loop strings = ["foo","bar","baz"] for s in strings println(s) end 33
- 34. Rand() rand(): 隨機0~1 rand([]): 從裡面選一個出來 y = rand([1, 2, 3]) 34
- 35. Array homogenous start from 1 mutable [ ]2 3 5 A = [2, 3, 5] A[2] # 3 35
- 36. 多維陣列 A = [0 -1 1; 1 0 -1; -1 1 0] A[1, 2] 36
- 37. 函式 function add(a, b) c = a + b return c end 37
- 38. 數值運算 介紹各種Array函式 zeros(Float64, 2, 2) # 2-by-2 matrix with 0 ones(Float64, 3, 3) # 3-by-3 matrix with 1 trues(2, 2) # 2-by-2 matrix with true eye(3) # 3-by-3 diagnal matrix rand(2, 2) # 2-by-2 matrix with random number 38
- 40. Comprehension [x for x = 1:3] [x for x = 1:20 if x % 2 == 0] ["$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“ ...] 40
- 41. Tuple Immutable tup = (1, 2, 3) tup[1] # 1 tup[1:2] # (1, 2) (a, b, c) = (1, 2, 3) 41
- 42. 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]) 42
- 43. 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"])) 43
- 45. 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) 45
- 46. 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 …… 46
- 47. Easy to profile Use @time ProfileView.view() 47
- 48. 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/ 48
- 49. Easy to parallelize for i = 1:100000 do_something() end @parallel for i = 1:100000 do_something() end 49
- 50. Built-in package manager julia> Pkg.update() julia> Pkg.add(“Foo”) julia> Pkg.rm(“Foo”) 50
- 51. @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 51
- 52. @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 52
- 54. 54
- 55. 55
- 56. 56
- 57. 57
- 58. 58
- 59. DataFrames.jl julia> using DataFrames julia> df = DataFrame(A = 1:4, B = ["M", "F", "F", "M"]) 4×2 DataFrames.DataFrame │ Row │ A │ B │ ├─────┼───┼───┤ │ 1 │ 1 │ M │ │ 2 │ 2 │ F │ │ 3 │ 3 │ F │ │ 4 │ 4 │ M │ 59
- 60. DataFrames.jl julia> df[:A] 4-element NullableArrays.NullableArray{Int64,1}: 1 2 3 4 julia> df[2, :A] Nullable{Int64}(2) 60
- 61. DataFrames.jl julia> df = CSV.read ("data.csv") julia> df = DataFrame(A = 1:10); julia> CSV.writetable("output.csv", df) 61
- 62. DataFrames.jl julia> names = DataFrame(ID = [1, 2], Name = ["John Doe", "Jane Doe"]) julia> jobs = DataFrame(ID = [1, 2], Job = ["Lawyer", "Doctor"]) julia> full = join(names, jobs, on = :ID) 2×3 DataFrames.DataFrame │ Row │ ID │ Name │ Job │ ├─────┼────┼──────────┼────────┤ │ 1 │ 1 │ John Doe │ Lawyer │ │ 2 │ 2 │ Jane Doe │ Doctor │ 62
- 63. Query.jl julia> q1 = @from i in dt begin @where i.age > 40 @select {number_of_children=i.children, i.name} @collect DataFrame end 63
- 64. 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) 64
- 65. 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) 65
- 66. 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) 66
- 67. GLM.jl 67 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 |
- 68. GLM.jl 68 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
- 69. GLM.jl 69 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
- 70. Gadfly.jl 70
- 71. Plots.jl 71 # 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
- 72. Data JuliaData DataFrames.jl CSV.jl DataStreams.jl CategoricalArrays.jl JuliaDB 72
- 73. File JuliaIO FileIO.jl JSON.jl LightXML.jl HDF5.jl GZip.jl 73
- 74. 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) 74
- 75. 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 75
- 76. Graph / Network JuliaGraphs LightGraphs.jl GraphPlot.jl 76
- 77. Plot Gadfly.jl JuliaPlots Plots.jl 77
- 78. Glue JuliaPy PyCall.jl pyjulia Conda.jl PyPlot.jl Pandas.jl Seaborn.jl SymPy.jl JuliaInterop RCall.jl JavaCall.jl CxxWrap.jl MATLAB.jl 78
- 79. Programming JuliaCollections Iterators.jl DataStructures.jl SortingAlgorithms.jl FunctionalCollections.jl Combinatorics.jl 79
- 80. Web JuliaWeb Requests.jl HttpServer.jl WebSockets.jl HTTPClient.jl 80
- 81. 跟其他語言的比較 Python R Perl 81
- 82. Jobs Apple, Amazon, Facebook, BlackRock, Ford, Oracle Comcast, Massachusetts General Hospital Farmers Insurance Los Alamos National Laboratory and the National Renewable Energy Laboratory 82 https://juliacomputing.com/press/2017/01/18/jobs.html
- 83. Julia Taiwan FB社群: https://www.facebook.com/groups/JuliaTaiwan/ 新知發布: https://www.facebook.com/juliannewstw/ 83
- 84. Backup 84
Editor's Notes
- #14: the next generation of macroeconomic models is very computationally intensive with large datasets and large numbers of variables
- #15: First, as free software Second, as the models that we use for forecasting and policy analysis grow more complicated, we need a language that can perform computations at a high speed
- #16: Fast and easy to code