intro-to-julia.jl

### A Pluto.jl notebook ###
# v0.19.39

using Markdown
using InteractiveUtils

# This Pluto notebook uses @bind for interactivity. When running this notebook outside of Pluto, the following 'mock version' of @bind gives bound variables a default value (instead of an error).
macro bind(def, element)
    quote
        local iv = try Base.loaded_modules[Base.PkgId(Base.UUID("6e696c72-6542-2067-7265-42206c756150"), "AbstractPlutoDingetjes")].Bonds.initial_value catch; b -> missing; end
        local el = $(esc(element))
        global $(esc(def)) = Core.applicable(Base.get, el) ? Base.get(el) : iv(el)
        el
    end
end

# ╔═╡ 60ea6a34-7d40-4527-a751-54ae0c691296
using PlutoUI

# ╔═╡ 33cf1e80-95f8-440f-8b10-f5ad180d94d4
# Why types are important in Julia

using BenchmarkTools

# ╔═╡ 9f6ac044-abd4-4c0f-a4a3-47081a925adb
using LinearAlgebra

# ╔═╡ 13aaeceb-e873-4865-a1c1-0d50251f7ed0
begin
	# Example of plots
	using Plots
	gr()    # for quick visualization
	# pythonplot() # Python styled
	# pgfplots()    # for publication quality
	
	# data
	x = (rand(100))
	y = x.^2
	
	#plot(x, y, label=:"Line", framestyle=[:box :grid])
	scatter(x, y, label="Scattered Data",legend=:topleft,
	         markersize=4, markercolor=:blue, 
	         markerstrokewidth=0, markeralpha=0.9)
	xaxis!("X-label"); xlims!(0,1); xticks!(-1:0.2:1)
	yaxis!("Y-label"); ylims!(0,1); yticks!(0:0.1:1)
	
	#savefig("examples/test01.pdf")
end

# ╔═╡ b7b978c9-10f9-41f9-abb2-cd44216165c4
begin
	# Example of plots
	using PythonPlot
	
	# gr()    # for quick visualization
	pythonplot() # Python styled
	#pgfplots()    # for publication quality
	
	# data same as above
	
	#plot(x, y, label=:"Line", framestyle=[:box :grid])
	PythonPlot.scatter(x, y, label="Scattered Data")
	xaxis!("X-label"); xlims!(0,1); xticks!(-1:0.2:1)
	yaxis!("Y-label"); ylims!(0,1); yticks!(0:0.1:1)
	
	#savefig("examples/test01.pdf")
end

# ╔═╡ e3c72b48-8d17-4b4e-bfcc-a615e8547672
using PlutoExtras

# ╔═╡ da266718-431f-4bcf-9c5b-e8e440e65029
using DifferentialEquations

# ╔═╡ 91b30a34-bc11-4d78-a9b2-2d2c7f964fc9
html"<button onclick='present()'>present</button>"

# ╔═╡ 9672457b-650d-4970-87f1-d4d501abb566
struct TwoColumn{A, B}
	left::A
	right::B
end

# ╔═╡ 188d2334-c6c0-43ab-92bb-33440e785687
function Base.show(io, mime::MIME"text/html", tc::TwoColumn)
	write(io,
		"""
		<div style="display: flex;">
			<div style="flex: 50%;">
		""")
	show(io, mime, tc.left)
	write(io,
		"""
			</div>
			<div style="flex: 50%;">
		""")
	show(io, mime, tc.right)
	write(io,
		"""
			</div>
		</div>
	""")
end

# ╔═╡ e3e52c62-d0d2-11ee-2402-df85ba2126b0
md"""
# Introduction to Julia Language
"""

# ╔═╡ 495e28d9-9a99-413b-8302-e334a47452ab
md"""
### Why Julia

- A reasonable compromise between slow, dynamic interpreted languages (e.g., Python) and fast, static compiled languages (e.g., C)
- Main focus is numerical computations, performance and ease of writing
- Robust package management and programming ecosystem
- It is time to move on from Fortran
"""

# ╔═╡ e1d9e83c-8179-4642-a626-0260eb5000f5
md"""
## [Download Julia](https://julialang.org/downloads/)
"""

# ╔═╡ 987c3716-b00d-4843-a294-23e723535675
LocalResource("/Users/pthakur8/workInbox/2024/workshops/intro-to-julia/julia_home.png")

# ╔═╡ 62e8a1db-94f0-45e6-9835-778fae3018c6
md"""
## Julia in a nutshell
##### Fast
Julia was designed for high performance. Julia programs automatically compile to efficient native code via LLVM, and support multiple platforms.

##### Dynamic
Julia is dynamically typed, feels like a scripting language, and has good support for interactive use, but can also optionally be separately compiled.

##### Reproducible
Reproducible environments make it possible to recreate the same Julia environment every time, across platforms, with pre-built binaries.

##### Composable
Julia uses multiple dispatch as a paradigm, making it easy to express many object-oriented and functional programming patterns. The talk on the Unreasonable Effectiveness of Multiple Dispatch explains why it works so well.

##### General
Julia provides asynchronous I/O, metaprogramming, debugging, logging, profiling, a package manager, and more. One can build entire Applications and Microservices in Julia.

##### Open source
Julia is an open source project with over 1,000 contributors. It is made available under the MIT license. The source code is available on GitHub.
"""

# ╔═╡ 1025dd46-3b73-4df7-9003-5a4c11a83037
md"""
## Create a virtual environment to work with
```julia
$ julia
  ]generate <package_name>
  ]activate <package_name>
  ]add Plots Pluto
```
### What this does?
```sh
➜ intro-to-julia tree intro_julia
intro_julia
├── Manifest.toml
├── Project.toml
└── src
    └── intro_julia.jl
```
"""

# ╔═╡ f82fa353-64e5-430a-8dd4-2a424d91c98b
md"""
## Run the [pluto notebook](https://plutojl.org/)

```julia
julia> using Pluto
julia> Pluto.run()
```

Pluto: very similar to jupyter notebook, but it is reactive, and easier version control.

#### Reactivity example:
"""

# ╔═╡ 11fa1cc8-f855-442e-afe1-9f2953f11d61
a = 7 # Changing `a` here automatically makes changes throughout the notebook

# ╔═╡ 4738b2c4-89ad-41ce-8c3f-e32c761c7ddf
b = a + 2

# ╔═╡ 59b0bda6-d406-4d1a-a559-23762a52646b
md"""
## Hello world!

We can use the base function `println()` to print stuff! 

"""

# ╔═╡ d37aa9ca-13f8-4d17-9cef-883618a4f22d
println("Hello, World!")

# ╔═╡ 55d4b6ea-e37e-48db-9234-d8bb031e92a1
md"""
## Data Types
**Static type system**: typical for compiled languages, where every expression must have a type computable before the execution of the program.

**Dynamic type system**: typical for interpreted languages, where the type of the expression is determined at run time, and nothing is known beforehand.

Julia has dynamic type system, and standard data types typical for most dynamic type programming languages:

* Primitive types: is a concrete type whose data consists of just bits.
    * Numeric types: `Int64, Float64, BigFloat, Complex`, etc.
    * `String` and `Char` for characters.

* Abstract types: `Any, Real, Number, Integer`. You can create your own abstract types as well. These are not instantiated, and only serve as describing sets of related types, i.e., they form a conceptual hierarchy but are not ascribed to a specific expression.

* Composite types: a collection of named fields, an instance of which can be treated as a single value.
    * `struct`

Julia is a functional programming language, so you don't have classes and objects. In pure object-oriented languages (e.g., Ruby and Smalltalk), all values are objects, whether they are composite or not. In C++/Java, you have objects and standalone types (e.g., `int` or `float`).

In Julia, all values are objects, but functions are not bundled with the objects they operate on.

"""

# ╔═╡ 48f8f5da-d034-484b-8d07-f275ba41027c
md"""
#### Abstract types

```julia
abstract type «name» end
abstract type «name» <: «supertype» end
```
The default supertype is `Any`. 

Examples:
```julia
abstract type Number end
abstract type Real          <: Number end
abstract type AbstractFloat <: Real end
abstract type Integer       <: Real end
```
"""

# ╔═╡ 32b771af-7cc3-49a7-8ee1-71fab5b79540
md"""
## Why types are important in Julia
"""

# ╔═╡ a6a9c9ac-b470-4222-81cf-95bd81113933
@btime begin
	x = rand(Int, 1000);
	sum_x = 0.0
	for i in x
		sum_x += i
	end
	sum_x
end

# ╔═╡ 6b94782f-204a-43b7-81eb-77d69c730fd1
@btime begin
	x = rand(Int, 1000);
	sum_x = 0
	for i in x
		sum_x += i
	end
	sum_x
end

# ╔═╡ 4ff83a18-3ae7-44db-8d35-2bcdbdfdc0c4
begin
	function myplus_typed(x::Int, y::Int)
		x+y
	end
	
	function myplus(x, y)
		x+y
	end
end

# ╔═╡ 87fda310-83f1-4d1b-9214-5e290eb98971
@btime begin
	x = rand(Int, 1000);
	sum_x = 0
	for i in x
		sum_x = myplus_typed(i,sum_x)
	end
	sum_x
end

# ╔═╡ aac2d40b-89b0-4180-a8b2-efed29d7cf99
@btime begin
	x = rand(Int, 1000);
	sum_x = 0.0
	for i in x
		sum_x = myplus(i,sum_x)
	end
	sum_x
end

# ╔═╡ 99f01a9b-a809-4979-af4d-643ac3eacec7
md"""
## Composite types:
```julia
struct Foo
    bar
    baz::Int
	qux::Float64
end
```
Struct is immutable by default, i.e., it cannot be modified after construction. 
We have a `mutable` keyword we can use before struct to make it modifiable.

"""

# ╔═╡ 08e1a92c-c057-4220-82ce-5bbb63e6b367
struct Foo
    bar
    baz::Int
	qux::Float64
end

# ╔═╡ 42d6adf5-c3aa-4021-9dea-dd5c1ecd3658
begin
	foo1 = Foo("Hello!", 23, 3.14)
	foo2 = Foo(83, 55, 1.57)
end

# ╔═╡ 4ef44902-49d0-4816-8251-48d07a28f60b
typeof(foo1)

# ╔═╡ 5943015b-ad71-410f-99f7-b11de783c28d
fieldnames(Foo)

# ╔═╡ 3dd4c845-1733-4d57-a880-7ffa6b85a76b
foo1.bar

# ╔═╡ 0b7ff119-cfdc-440e-a609-f1d0702bdfe7
foo2.bar

# ╔═╡ 0d6f1f9d-8bc6-488d-8738-a72341a184f7
md"""
## Mutable structs

Allows you to modify the fields after construction
"""

# ╔═╡ 44b5ddc2-534a-4c4e-992f-1f307c35f38f
mutable struct Bar
    baz
    qux::Float64
end

# ╔═╡ 10604ac1-cbaa-4662-baa8-df82b796a4b0
bar = Bar("Hello!", 1.5)

# ╔═╡ 73e0aea1-36e6-4473-a11c-66d540bfb552
bar.qux

# ╔═╡ 0d1ecc3f-8d73-444d-8ddc-60475681de9f
# Change the fields of the object bar
bar.qux = 2.5

# ╔═╡ f5388b1b-e86b-43f4-bb53-cec28fd2c6b1
bar

# ╔═╡ 7dfe6956-acb0-4897-bfea-e73c46c08420
md"""
## Constructors for a struct

Constructors are functions that create new objects: specifically, instances of Composite types. 

The examples above are outer constructor methods. 

While Julia is not purely object-oriented, it allows us to define inner constructor methods (functions) within a struct. Thus, most of our object-oriented needs are taken care of.

Additionally, inner methods have access to a special local function `new()` that creates objects of the same type as the struct.

"""

# ╔═╡ db765ef0-caed-49d5-86a3-5408bea3035d
struct Square 
    height::Int
    width::Int
    area::Int
    
    function Square(h, w)
        a = h * w
        
        return new(h, w, a)
    end 
end 

# ╔═╡ 3fa8cb34-0703-46e8-ac22-a327626bc987
sq = Square(5,3)

# ╔═╡ c6d8ac20-fa3b-44fb-a7e0-f57ff8820821
sq.area

# ╔═╡ d7c3d3ca-975e-4bda-9617-67bf8ab25cc0
##sq2 = Square(2,5,10)

# ╔═╡ 0a876d5c-e2c1-49af-b8eb-43918186a100
md"""
## Collections in Julia

* Array (and Vector and Matrix)
* Tuple (and NamedTuple)
* Set
* Dict
"""

# ╔═╡ db90a28d-cd3b-445d-960c-705fd536efbb
md"""
#### Array type
```julia
a = [4, 3, 1]    	# create 1-dimensional Array (i.e., Vector)
B = [4 5 6; 1 2 3]  # create 2-dimensional Array (i.e., Matrix)
```

##### Useful constructors:
Use `LinearAlgebra` library for some more fancy matrices
```julia
zeros(type, n,m) # nxm matrix of zeros
ones(type, n,m)  # nxm matrix of ones
I(n)             # n-dimensional identity matrix
falses(n,m)      # array of falses, similar to zeros
trues(n,m)       # array of trues, similar to ones
rand(type, n,m)  # array of random numbers, sampled from uniform distribution
randn(type, n,m) # sampled from normal distribution
```

Array indexing starts from 1
```
a = rand(5,5)
a[2:3, 4]    # will return 2x1 array, 2nd and 3rd column of 4th row
```

"""

# ╔═╡ 759e3317-d5ec-4324-8556-9c399518a6dc
zeros(5)

# ╔═╡ d20a96ab-8715-42cf-aed3-006bd02d0af4
zeros(Int,5)

# ╔═╡ 5c606960-9965-4464-a5ed-60e0b9491ecb
I(5)

# ╔═╡ d3d4e6c7-18bc-4a72-b3c8-6adc83e567fe
falses(5,2)

# ╔═╡ f6c5d603-56b0-4a75-8022-d91f3224f192
matrix1 = rand(5,5)

# ╔═╡ 266c2092-1b9f-4fd6-9bd2-3935b747fc5d
matrix1[2:3,4]

# ╔═╡ 4b79c499-1fb3-4f0e-84f5-25b9268b1feb
md"""
## Vectorized dot `.` operator

For every binary operation (e.g., `+, -, ^`) there is a corresponding operation (`.+, .-, .^`) to perform element-wise operation on arrays and matrices.

These are vectorized, and perform a broadcast operation. That is, this operator applies the given function element-wise, without using extra memory.

"""

# ╔═╡ f7f5ff8e-5c95-476a-8027-801ff6a4b65f
vec1 = 1:5

# ╔═╡ 4a510c79-17b3-4597-a7bc-11d10814ccb6
vec2 = vec1 .^2

# ╔═╡ 99690d03-7621-41f5-bbca-f5ef0a0a1687
vec2 .> 10

# ╔═╡ 72af35fe-546a-48a5-b0ae-4e0dac6bfe36
vec2[vec2 .> 10]

# ╔═╡ d3db7943-27fb-44f8-bee9-c4431427b399
md"""
## Tuples
Fixed length, immutable, can hold heterogeneous data
```julia
tuple1 = (3.14, "pie")	# Create tuple with 2 elements
tuple1[2]    # access elements
```

**Named tuple**
```julia
ntuple1 = (firstname = "Prithvi", lastname = "Thakur", id = 25)

# Can be accessed via name
ntuple1.firstname

# or via index
ntuple1[2]
```
"""

# ╔═╡ 75c9ab4b-caf8-4783-a9dd-33285eb8cd2a
ntuple1 = (firstname = "Prithvi", lastname = "Thakur", id = 25)

# ╔═╡ a59a94e3-379a-4ce3-8b0a-0e42f1a5db20
ntuple1[2]

# ╔═╡ 5cb652a5-25bf-465a-8745-41e798c6917d
md"""
## Sets
* Sets have efficient implementations of set operations such as in, union, intersection, symmetric difference, subset, etc. 
* Elements in a Set are unique.
* Not ordered.
"""

# ╔═╡ c56679e6-cb34-4fd3-932b-d92c938e0135
begin
	set1 = Set([1,2, 2, 3, 4, 5])
	set2 = Set([3,5,7,9])
end

# ╔═╡ c9319016-5209-40d7-b106-8f51a7b3547c
intersect(set1, set2)

# ╔═╡ 2621f286-f4d9-430a-96e5-1e62fc5f382e
set1

# ╔═╡ 507001fc-b643-4029-88f6-e5155cb16201
md"""
## Dictionary `Dict` type
* (Key, Value) pair

Tuples are cheaper to construct than Dicts. Order is not important in Dict.
"""

# ╔═╡ dd481e6f-373b-4821-8c7e-62d4381ba0eb
dict1 = Dict("a" => 21, "b" => 25, "c" => 37)

# ╔═╡ 1936fe1f-4229-4c40-b836-3e273749aa9b
dict1["c"]

# ╔═╡ 782925e7-4de8-4157-86af-b895740b5c4e
md"""
## Functions (aka methods)
Conventional syntax:
```julia
function <name>(arguments)
	operations
	return value
end
```

Mathematical (or functional language) syntax, conventionally used for single-line functions:
```julia
f(x) = return value # where x is the input argument
```
"""

# ╔═╡ 323cfc3b-edfb-4892-8ef6-23f7465f5974
function add_one(n)
	return n .+ 1
end

# ╔═╡ 9e3e00ba-4e7a-469f-ba16-4a35cc8dcd3c
f(x) = x + 1

# ╔═╡ e73fac51-33f2-4fd0-b146-c0f40867cd61
add_one(5)

# ╔═╡ e594d69c-e8f6-480c-9aa4-40e1ebc9aeaa
add_one(rand(5))

# ╔═╡ 02664a66-233b-4ed7-a5e6-02671a2553b4
md"""
## `!` notation: functions that modify the input
Similar to passing by reference in C++. Using this type of function will modify the input itself.

Obviously, this will not work for immutable types.
"""

# ╔═╡ 82a3a959-24e2-4805-bbf3-0c67fcfdb5c3
function add_one!(x)
    x .= x .+ 1
end

# ╔═╡ e2a44032-0e9a-4495-bdf0-2d2dc99de8c9
begin
	var1 = [5,6,7]
	var2 = [1,2,3]
end

# ╔═╡ dcd3901d-59a0-4b96-b564-de2397ffc246
add_one(var1)

# ╔═╡ c3ad4e71-ff2b-41ed-8be0-142097b974f4
var1

# ╔═╡ 21d65a37-1c94-4828-a1d7-f1dbe157fdbd
add_one!(var2)

# ╔═╡ 5619aedf-9359-4938-8974-5e1d611c97a0
var2

# ╔═╡ 5547dad3-0ed3-45b5-9fc9-655896155fe8
md"""
## Plots:
Very similar to python, easy and convenient for 2D plots.
[Plots.jl](https://docs.juliaplots.org/latest/) provides a convenient way to switch backends without altering the code.
"""

# ╔═╡ 6a96e890-6637-4acd-9293-aad79ebe820c


# ╔═╡ 1b5461f3-2423-4277-b577-7c11a55dca2f
md"""
## Julia has a growing and robust ecosystem for numerical methods and solutions

#### Example: using DifferentialEquations.jl to solve lorenz equation
The Lorenz equations are given by:
"""

# ╔═╡ 1da6085f-4f3e-4278-b2d1-32712bc6b205
texeq"\frac{dx}{dt} = \sigma(y - x)"

# ╔═╡ b14c1316-d75a-495f-8b3c-5cc906e6cf55
texeq"\frac{dy}{dt} = x(\rho - z) - y"

# ╔═╡ a38dc093-35c8-40f1-a294-aa22ede230e1
texeq"\frac{dz}{dt} = xy - \beta z"

# ╔═╡ f97f8175-88de-46d9-8ec2-2ebf6bbb2228
begin
	function lorenz!(du, u, p, t)
    	σ, ρ, β = p
    	du[1] = σ * (u[2] - u[1])
    	du[2] = u[1] * (ρ - u[3]) - u[2]
    	du[3] = u[1] * u[2] - β * u[3]
	end
end

# ╔═╡ 9c5cc745-47eb-41c0-9c69-6eabf7fc7189
# Initial conditions and parameters
begin
	u0 = [1.0, 0.0, 0.0]
	p = [10.0, 28.0, 8/3]
end

# ╔═╡ 76694655-1cea-4aef-9c07-6f73e6967b29
# Solve the differential equations
begin
	tspan = (0.0, 100.0)
	prob = ODEProblem(lorenz!, u0, tspan, p)
	sol = solve(prob)
end

# ╔═╡ 87d59413-2389-47ba-bea4-520fe6db3280
# Plot the solution
begin
	# @bind sol
	Plots.plot(sol, idxs=(1,2,3))
end

# ╔═╡ 00000000-0000-0000-0000-000000000001
PLUTO_PROJECT_TOML_CONTENTS = """
[deps]
BenchmarkTools = "6e4b80f9-dd63-53aa-95a3-0cdb28fa8baf"
DifferentialEquations = "0c46a032-eb83-5123-abaf-570d42b7fbaa"
LinearAlgebra = "37e2e46d-f89d-539d-b4ee-838fcccc9c8e"
Plots = "91a5bcdd-55d7-5caf-9e0b-520d859cae80"
PlutoExtras = "ed5d0301-4775-4676-b788-cf71e66ff8ed"
PlutoUI = "7f904dfe-b85e-4ff6-b463-dae2292396a8"
PythonPlot = "274fc56d-3b97-40fa-a1cd-1b4a50311bf9"

[compat]
BenchmarkTools = "~1.5.0"
DifferentialEquations = "~7.13.0"
Plots = "~1.40.3"
PlutoExtras = "~0.7.12"
PlutoUI = "~0.7.58"
PythonPlot = "~1.0.3"
"""

# ╔═╡ 00000000-0000-0000-0000-000000000002
PLUTO_MANIFEST_TOML_CONTENTS = """
# This file is machine-generated - editing it directly is not advised

julia_version = "1.9.3"
manifest_format = "2.0"
project_hash = "2e828298b9e0dc7af8ada113a4ef22f0efeb32c1"

[[deps.ADTypes]]
git-tree-sha1 = "016833eb52ba2d6bea9fcb50ca295980e728ee24"
uuid = "47edcb42-4c32-4615-8424-f2b9edc5f35b"
version = "0.2.7"

[[deps.AbstractPlutoDingetjes]]
deps = ["Pkg"]
git-tree-sha1 = "0f748c81756f2e5e6854298f11ad8b2dfae6911a"
uuid = "6e696c72-6542-2067-7265-42206c756150"
version = "1.3.0"

[[deps.Adapt]]
deps = ["LinearAlgebra", "Requires"]
git-tree-sha1 = "cde29ddf7e5726c9fb511f340244ea3481267608"
uuid = "79e6a3ab-5dfb-504d-930d-738a2a938a0e"
version = "3.7.2"
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version = "1.5.8+0"

[[deps.mtdev_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
git-tree-sha1 = "814e154bdb7be91d78b6802843f76b6ece642f11"
uuid = "009596ad-96f7-51b1-9f1b-5ce2d5e8a71e"
version = "1.1.6+0"

[[deps.nghttp2_jll]]
deps = ["Artifacts", "Libdl"]
uuid = "8e850ede-7688-5339-a07c-302acd2aaf8d"
version = "1.48.0+0"

[[deps.p7zip_jll]]
deps = ["Artifacts", "Libdl"]
uuid = "3f19e933-33d8-53b3-aaab-bd5110c3b7a0"
version = "17.4.0+0"

[[deps.x264_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
git-tree-sha1 = "4fea590b89e6ec504593146bf8b988b2c00922b2"
uuid = "1270edf5-f2f9-52d2-97e9-ab00b5d0237a"
version = "2021.5.5+0"

[[deps.x265_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
git-tree-sha1 = "ee567a171cce03570d77ad3a43e90218e38937a9"
uuid = "dfaa095f-4041-5dcd-9319-2fabd8486b76"
version = "3.5.0+0"

[[deps.xkbcommon_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Wayland_jll", "Wayland_protocols_jll", "Xorg_libxcb_jll", "Xorg_xkeyboard_config_jll"]
git-tree-sha1 = "9c304562909ab2bab0262639bd4f444d7bc2be37"
uuid = "d8fb68d0-12a3-5cfd-a85a-d49703b185fd"
version = "1.4.1+1"
"""

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