You will see much more of the Distributions.jl package in this course. See also:
mimetext/htmlrootassigneelast_run_timestampA}* o persist_js_state·has_pluto_hook_features§cell_id$f72045aa-fa31-40bf-b80c-5259583f1d30depends_on_disabled_cells§runtime cBpublished_object_keysdepends_on_skipped_cells§errored$ccbf4589-8d25-434e-a7f4-3d972b4ee078queued¤logsrunning¦outputbody1×4 Matrix{Int64}:
1 2 3 4mimetext/plainrootassigneewlast_run_timestampA}*
Packages
The base form of Julia has many wonderful functions and methods. But not everything. To extend functionality, we have to import additional software packages. Below is a list of the few packages we cover in today's tutorial. But you'll see more later in the course.
When you call a function that Julia doesn't know, it will return a list of the steps it took to execute your command and point to where its progress was blocked. This is highly useful but it typically requires a bit of practice to parse (i.e., read and filter) stack traces.
MethodError
Suppose we write a function that expects an Integer input and call that function with an Float64 argument:
Julia also has a Symbol type, which is used for meta-programming (not important for this course). A Symbol type is characterized by a : in front of a word. For example:
This notebook will teach you some of the basic programming routines in Julia. You will need these skills to complete the probabilistic programming assignments later on in the course. We will assume basic familiarity with programming, such as for-loops, if-else statements and function definitions.
Resources:
Julia Basics from "Julia Programming for Machine Learning" taught at TU Berlin:
Macros are a somewhat advanced form of metaprogramming. You will not need to define any new macros; this instruction is just here to explain what they are.
The course is built in Pluto.jl, a reactive programming environment. Pluto notebooks are wonderfully intuitive and interactive, and are already revolutionizing mathematics and computer science education (e.g., 18.S191 Computational Thinking @MIT).
A few things to be aware of when working in Pluto notebooks:
Code is not executed sequentially. In other words, you can call a variable in a cell even if that variable is defined in a later cell.
You cannot re-use variable names, i.e., you cannot overwrite a variable with a different variable in a latter cell.
A cell can only execute a single function/instruction; if you want to execute more instructions, you have to wrap them in a begin .. end environment.
Each Pluto notebook manages its own software packages (more on that later).
The Live docs button on the bottom-right corner can be used to look up documentation of functions.
The Status button on the bottom-right corner displays what the kernel is doing in the background.
You will not have to use Symbols in the course, but you may see one every once in a while in the lecture notes. For example, the plot command (see Visualization section), may have a markershape=:cross argument.
plot and scatter are the most useful commands. A scatter command will ignore properties such as linewidth and linestyle (since there are no lines) and will listen to markersize and markershape commands (see Supported Attributes in the API).
mimetext/htmlrootassigneelast_run_timestampA}* لpersist_js_state·has_pluto_hook_features§cell_id$755d9324-5447-4240-9a17-6e212dab4edddepends_on_disabled_cells§runtime published_object_keysdepends_on_skipped_cells§errored$3d89c37f-0876-4ba1-aa35-0a7273d4d269queued¤logsrunning¦outputbodyprefixInt64elements1text/plain2text/plain3text/plain4text/plaintypeArrayprefix_shortobjectid3048a8fb84aec90bmime!application/vnd.pluto.tree+objectrootassigneevlast_run_timestampA}*CodeInstance for MethodInstance for give_magic_number(::Int64)inlined£urlpathb/home/runner/work/course/course/probprog/Intro to Julia.jl#==#b6399549-c754-498a-887c-401f252ba21fsource_packagecall>CodeInstance for MethodInstance for give_magic_number(::Int64)linfo_typeCore.CodeInstancelinefile9Intro to Julia.jl#==#b6399549-c754-498a-887c-401f252ba21ffuncgive_magic_numberparent_modulefrom_ccall_shortmacro expansioninlinedãurlpathb/home/runner/work/course/course/probprog/Intro to Julia.jl#==#794970ef-f2d2-4dc8-ae43-2b1ecc306a74source_packagecallmacro expansionlinfo_typeNothinglinefile9Intro to Julia.jl#==#794970ef-f2d2-4dc8-ae43-2b1ecc306a74funcmacro expansionparent_modulefrom_c«plain_errorUndefVarError: `kl` not defined in `Main.var"workspace#3"`
Suggestion: check for spelling errors or missing imports.
Stacktrace:
[1] give_magic_number(x::Int64)
@ Main.var"workspace#3" ~/work/course/course/probprog/Intro to Julia.jl#==#b6399549-c754-498a-887c-401f252ba21f:4
[2] macro expansion
@ ~/work/course/course/probprog/Intro to Julia.jl#==#794970ef-f2d2-4dc8-ae43-2b1ecc306a74:1 [inlined]mime'application/vnd.pluto.stacktrace+objectrootassigneelast_run_timestampA}*Fnpersist_js_state·has_pluto_hook_features§cell_id$794970ef-f2d2-4dc8-ae43-2b1ecc306a74depends_on_disabled_cells§runtimepublished_object_keysdepends_on_skipped_cells§errored$5905847d-2358-4380-a5a0-c5ac8c716839queued¤logsrunning¦outputbody0.10798193302637613mimetext/plainrootassigneelast_run_timestampA}*ADpersist_js_state·has_pluto_hook_features§cell_id$5905847d-2358-4380-a5a0-c5ac8c716839depends_on_disabled_cells§runtimee?published_object_keysdepends_on_skipped_cells§errored$277c5574-910b-4f05-8661-ef81278e9319queued¤logsrunning¦outputbody
Control flow refers to redirecting how a compiler goes through a program. Instead of traversing it line-by-line, things like if-else statements can make a compiler skip steps. These require logical operations: you can use == to check if two variables have the same value, === to check if they are actually the same object (i.e., same memory reference) and != to check if they're not equal.
Function and expressions are a core component of the julia language. Its "multiple dispatch" feature means that you can define multiple functions with the same name but with behaviour that depends on the input argument types. When you're starting out, you may not notice this so much, but you will start to appreciate this feature tremendously when you begin to professionally develop software.
// Load the library for consistent smooth scrolling
const {default: scrollIntoView} = await import("data:text/javascript;base64,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")
const indent = true
const aside = true
const title_text = "Table of Contents"
const include_definitions = false
const tocNode = html``
tocNode.classList.toggle("aside", aside)
tocNode.classList.toggle("indent", indent)
const getParentCell = el => el.closest("pluto-cell")
const getHeaders = () => {
const depth = Math.max(1, Math.min(6, 3)) // should be in range 1:6
const range = Array.from({length: depth}, (x, i) => i+1) // [1, ..., depth]
const selector = [
...(include_definitions ? [
`pluto-notebook pluto-cell .pluto-docs-binding`,
`pluto-notebook pluto-cell assignee:not(:empty)`,
] : []),
...range.map(i => `pluto-notebook pluto-cell h${i}`)
].join(",")
return Array.from(document.querySelectorAll(selector)).filter(el =>
// exclude headers inside of a pluto-docs-binding block
!(el.nodeName.startsWith("H") && el.closest(".pluto-docs-binding")) && !el.classList.contains("no-toc")
)
}
const document_click_handler = (event) => {
const path = (event.path || event.composedPath())
const toc = path.find(elem => elem?.classList?.contains?.("toc-toggle"))
if (toc) {
event.stopImmediatePropagation()
toc.closest(".plutoui-toc").classList.toggle("hide")
}
}
document.addEventListener("click", document_click_handler)
const header_to_index_entry_map = new Map()
const currently_highlighted_set = new Set()
const last_toc_element_click_time = { current: 0 }
const intersection_callback = (ixs) => {
let on_top = ixs.filter(ix => ix.intersectionRatio > 0 && ix.intersectionRect.y < ix.rootBounds.height / 2)
if(on_top.length > 0){
currently_highlighted_set.forEach(a => a.classList.remove("in-view"))
currently_highlighted_set.clear()
on_top.slice(0,1).forEach(i => {
let div = header_to_index_entry_map.get(i.target)
div.classList.add("in-view")
currently_highlighted_set.add(div)
/// scroll into view
/*
const toc_height = tocNode.offsetHeight
const div_pos = div.offsetTop
const div_height = div.offsetHeight
const current_scroll = tocNode.scrollTop
const header_height = tocNode.querySelector("header").offsetHeight
const scroll_to_top = div_pos - header_height
const scroll_to_bottom = div_pos + div_height - toc_height
// if we set a scrollTop, then the browser will stop any currently ongoing smoothscroll animation. So let's only do this if you are not currently in a smoothscroll.
if(Date.now() - last_toc_element_click_time.current >= 2000)
if(current_scroll < scroll_to_bottom){
tocNode.scrollTop = scroll_to_bottom
} else if(current_scroll > scroll_to_top){
tocNode.scrollTop = scroll_to_top
}
*/
})
}
}
let intersection_observer_1 = new IntersectionObserver(intersection_callback, {
root: null, // i.e. the viewport
threshold: 1,
rootMargin: "-15px", // slightly smaller than the viewport
// delay: 100,
})
let intersection_observer_2 = new IntersectionObserver(intersection_callback, {
root: null, // i.e. the viewport
threshold: 1,
rootMargin: "15px", // slightly larger than the viewport
// delay: 100,
})
const render = (elements) => {
header_to_index_entry_map.clear()
currently_highlighted_set.clear()
intersection_observer_1.disconnect()
intersection_observer_2.disconnect()
let last_level = `H1`
return html`${elements.map(h => {
const parent_cell = getParentCell(h)
let [className, title_el] = h.matches(`.pluto-docs-binding`) ? ["pluto-docs-binding-el", h.firstElementChild] : [h.nodeName, h]
const id = title_el.matches("assignee") ?
title_el.innerText.replace(/^const /, "") :
title_el.id ?
title_el.id :
parent_cell.id
const inner_html = title_el.innerHTML
const a = html`${inner_html}`
/* a.onmouseover=()=>{
parent_cell.firstElementChild.classList.add(
'highlight-pluto-cell-shoulder'
)
}
a.onmouseout=() => {
parent_cell.firstElementChild.classList.remove(
'highlight-pluto-cell-shoulder'
)
} */
a.onclick=(e) => {
e.preventDefault();
history.replaceState(null, null, a.href)
last_toc_element_click_time.current = Date.now()
scrollIntoView(h, {
behavior: 'smooth',
block: 'start',
}).then(() =>
// sometimes it doesn't scroll to the right place
// solution: try a second time!
scrollIntoView(h, {
behavior: 'smooth',
block: 'start',
})
)
}
// Remove any `id` attributes recursively, because they may interfere with linking-to-id using `#`
const removeIdAttributes = (el) => {
if (el && el.nodeType === 1) { // Element node
if (el.hasAttribute?.("id")) el.removeAttribute?.("id")
el.childNodes.forEach(removeIdAttributes)
}
}
removeIdAttributes(a)
// Remove Click-To-Copy-Header-ID feature
a.querySelectorAll("pluto-header-id-copy-wrapper").forEach(el => el.remove())
const row = html`
${a}
`
intersection_observer_1.observe(title_el)
intersection_observer_2.observe(title_el)
header_to_index_entry_map.set(title_el, row)
if(className.startsWith("H"))
last_level = className
return row
})}`
}
const invalidated = { current: false }
const updateCallback = () => {
if (!invalidated.current) {
tocNode.querySelector("section").replaceWith(
html`${render(getHeaders())}`
)
}
}
updateCallback()
setTimeout(updateCallback, 100)
setTimeout(updateCallback, 1000)
setTimeout(updateCallback, 5000)
const notebook = document.querySelector("pluto-notebook")
// We have a mutationobserver for each cell:
const mut_observers = {
current: [],
}
const createCellObservers = () => {
mut_observers.current.forEach((o) => o.disconnect())
mut_observers.current = Array.from(notebook.querySelectorAll("pluto-cell")).map(el => {
const o = new MutationObserver(updateCallback)
o.observe(el, {attributeFilter: ["class"]})
return o
})
}
createCellObservers()
// And one for the notebook's child list, which updates our cell observers:
const notebookObserver = new MutationObserver(() => {
updateCallback()
createCellObservers()
})
notebookObserver.observe(notebook, {childList: true})
// And finally, an observer for the document.body classList, to make sure that the toc also works when it is loaded during notebook initialization
const bodyClassObserver = new MutationObserver(updateCallback)
bodyClassObserver.observe(document.body, {attributeFilter: ["class"]})
// Hide/show the ToC when the screen gets small
let match_listener = () => {
const small = (tocNode.closest("pluto-editor") ?? document.body).scrollWidth < 1000
tocNode.classList.toggle("smallscreen", small)
tocNode.classList.toggle("hide", small)
}
for(let s of [1000, 1100, 1200, 1300, 1400, 1500, 1600, 1700, 1800, 1900, 2000]) {
let m = matchMedia(`(max-width: ${s}px)`)
m.addListener(match_listener)
invalidation.then(() => m.removeListener(match_listener))
}
match_listener()
invalidation.then(() => {
invalidated.current = true
intersection_observer_1.disconnect()
intersection_observer_2.disconnect()
notebookObserver.disconnect()
bodyClassObserver.disconnect()
mut_observers.current.forEach((o) => o.disconnect())
document.removeEventListener("click", document_click_handler)
})
return tocNode
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You may be familiar with "list comprehension", which is a shortened form of iterating through a collection:
Numbers in Julia have specific types, most notably Integer, Real and Complex. (See this documentation page for the full type tree.) It is important to be aware of what type your numbers are because many functions operate differently on different number types.
mimetext/htmlrootassigneelast_run_timestampA}* 2persist_js_state·has_pluto_hook_features§cell_id$02c03dad-d974-4584-9766-0e7ea79047e0depends_on_disabled_cells§runtime :published_object_keysdepends_on_skipped_cells§errored$721d9bd7-c04c-4874-897e-61fde49ba257queued¤logsrunning¦outputbody#fn (generic function with 1 method)mimetext/plainrootassigneelast_run_timestampA}*=y[persist_js_state·has_pluto_hook_features§cell_id$721d9bd7-c04c-4874-897e-61fde49ba257depends_on_disabled_cells§runtime published_object_keysdepends_on_skipped_cells§errored$14e2c87f-557e-45fa-8036-464d5b4deac5queued¤logsrunning¦outputbodyٮ
You should read this as "there exists a function called add1 that expects an Integer input." Try that.
The red highlighting of ::Integer is also important but requires a slightly more complicated example. Suppose we have a function with two Integer inputs and we call with Float64 and Int64 arguments.
Below are some examples of importing packages and using their added functionalities.
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The function `add1` exists, but no method is defined for this combination of argument types.
[0mClosest candidates are:
[0m add1([91m::Integer[39m)
[0m[90m @[39m [35mMain.var"workspace#3"[39m [90m~/work/course/course/probprog/[39m[90m[4mIntro to Julia.jl#==#113fa658-4325-4ea6-a5ab-6337889006f4:1[24m[39m
stacktracecall_shortmacro expansioninlinedãurlpathb/home/runner/work/course/course/probprog/Intro to Julia.jl#==#897d515d-bfda-4a8f-abbb-9276d69f0f4dsource_packagecallmacro expansionlinfo_typeNothinglinefile9Intro to Julia.jl#==#897d515d-bfda-4a8f-abbb-9276d69f0f4dfuncmacro expansionparent_modulefrom_c«plain_errorMethodError: no method matching add1(::Float64)
The function `add1` exists, but no method is defined for this combination of argument types.
Closest candidates are:
add1(!Matched::Integer)
@ Main.var"workspace#3" ~/work/course/course/probprog/Intro to Julia.jl#==#113fa658-4325-4ea6-a5ab-6337889006f4:1
Stacktrace:
[1] macro expansion
@ ~/work/course/course/probprog/Intro to Julia.jl#==#897d515d-bfda-4a8f-abbb-9276d69f0f4d:1 [inlined]mime'application/vnd.pluto.stacktrace+objectrootassigneelast_run_timestampA}*F1persist_js_state·has_pluto_hook_features§cell_id$897d515d-bfda-4a8f-abbb-9276d69f0f4ddepends_on_disabled_cells§runtimepublished_object_keysdepends_on_skipped_cells§errored$ebbf4498-4082-44a0-a904-c80ca6dab2c7queued¤logsrunning¦outputbody$1×2 Matrix{Float64}:
1.0 0.333333mimetext/plainrootassigneelast_run_timestampA}*>7&persist_js_state·has_pluto_hook_features§cell_id$ebbf4498-4082-44a0-a904-c80ca6dab2c7depends_on_disabled_cells§runtimeHipublished_object_keysdepends_on_skipped_cells§errored$2bad907d-5859-4465-8ed6-4285642d9874queued¤logsrunning¦outputbody
Note that we first of all get a MethodError. This points to the fact that Julia could not find the function (i.e, method) that you asked for; add1(::Float64) does not exist.
Furthermore, Julia provides a list of "Closest candidates" which are functions of the same name with different input arguments. It reports:
mimetext/htmlrootassigneelast_run_timestampA}* Жpersist_js_state·has_pluto_hook_features§cell_id$2bad907d-5859-4465-8ed6-4285642d9874depends_on_disabled_cells§runtime 0͵published_object_keysdepends_on_skipped_cells§errored$660571c4-3d5e-4eba-b6d9-bcab17c2a2eequeued¤logsrunning¦outputbodyProgramming in Juliamimetext/htmlrootassigneelast_run_timestampA}*;'persist_js_state·has_pluto_hook_features§cell_id$660571c4-3d5e-4eba-b6d9-bcab17c2a2eedepends_on_disabled_cells§runtime͗published_object_keysdepends_on_skipped_cells§errored$4f785723-2f6a-4dcd-82a7-8d15daf191e8queued¤logsrunning¦outputbodyJ
What to do with errors?
To summarize, when you get an error, it is important to take your time, and read the message. If you want to know where something happened, look at the stack trace. Try to see an error message as positive feedback: you are on the right track, and Julia is trying to help you to write the correct code.
The type of error can also be informative. The MethodError is probably the error you will see most often.
We again get the MethodError that the function we asked for doesn't exist and a suggested alternative (i.e., "closest candidate"). But this time, only the first argument ::Integer is highlighted in red.
Julia checks your input argument types against those in the closest candidates. This tells you what to change: the solution would be to either:
Change the call: Make the first argument of your function call to an Integer type. That would be add(3, 4).
Change the defintion: Make the function accept a more general Real number as the first argument.
Matrices can be constructed by separating elements with spaces and rows by semicolons:
mimetext/htmlrootassigneelast_run_timestampA}* /persist_js_state·has_pluto_hook_features§cell_id$895960bf-1ee2-4aa8-b38c-5857525b1ddcdepends_on_disabled_cells§runtime Cpublished_object_keysdepends_on_skipped_cells§errored$08b24136-c292-4360-a90e-a8fd82d45d6bqueued¤logsrunning¦outputbody$add (generic function with 1 method)mimetext/plainrootassigneelast_run_timestampA}*F?Ȱpersist_js_state·has_pluto_hook_features§cell_id$08b24136-c292-4360-a90e-a8fd82d45d6bdepends_on_disabled_cells§runtime published_object_keysdepends_on_skipped_cells§errored$e3be7db2-a307-4083-bb35-db4e70dfe1bfqueued¤logsrunning¦outputbodyj
Plots.jl provides a common interface to call various other visualization backends (GR, Matplotlib, PGFPlotsX, Plotly, etc.). In other words, commands like plot(..) will be translated into the appropriate command for the backend. So, it does not re-invent the wheel but rather gives you access to the already enormous field of visualization tools.
Below are a few examples of the most common visualization commands you'll see throughout the course. The core principle is to use a plot type as base command and then provide keyword arguments (in String, Number or Symbol type) to apply variations.
Words that start with the @ symbol are macros in Julia, for example @time, @test, @model. They represent a series of functions called on an input structure and are really handy when you have to use the same set of instructions often.
For example, you could define a ProgressMeter bar, update it at every iteration of a for-loop and write a custom print statement every time. Or, you could call the @showprogress macro on the for-loop itself:
Simple if-else statements can often be replaced by ternary checks. Essentially, you ask a question (a logical operation followed by ?) and then tell the program what to do when the answer is yes (written immediately after the question) or no (written after the yes-answer followed by a :).
Functions that modify their input arguments instead of creating new output variables are typically marked with an !. Below I have defined an unsorted vector and I call sort to sort it in increasing order. If I call the sort function and the original vector, then they will be different:
Int64 is a 64-byte integer. Other options are 32-,16-, or 8-bit integers and they can be unsigned as well. The default real-valued numbers is a 64-bit floating-point number:
Arrays are indexed with square brackets, A[i,j]. You can construct a matrix by enclosing a set of numbers with square brackets. If you separate your numbers with comma's, then you will get a column vector:
mimetext/htmlrootassigneelast_run_timestampA}* [persist_js_state·has_pluto_hook_features§cell_id$77f5b5de-040f-4406-bb57-c1fe58e3b32bdepends_on_disabled_cells§runtime +published_object_keysdepends_on_skipped_cells§errored$0e341cb6-bbca-4581-858f-50b4e2ca858aqueued¤logsrunning¦outputbodymsgMethodError: no method matching add(::Float64, ::Int64)
The function `add` exists, but no method is defined for this combination of argument types.
[0mClosest candidates are:
[0m add([91m::Integer[39m, ::Integer)
[0m[90m @[39m [35mMain.var"workspace#3"[39m [90m~/work/course/course/probprog/[39m[90m[4mIntro to Julia.jl#==#08b24136-c292-4360-a90e-a8fd82d45d6b:1[24m[39m
stacktracecall_shortmacro expansioninlinedãurlpathb/home/runner/work/course/course/probprog/Intro to Julia.jl#==#0e341cb6-bbca-4581-858f-50b4e2ca858asource_packagecallmacro expansionlinfo_typeNothinglinefile9Intro to Julia.jl#==#0e341cb6-bbca-4581-858f-50b4e2ca858afuncmacro expansionparent_modulefrom_c«plain_errorMethodError: no method matching add(::Float64, ::Int64)
The function `add` exists, but no method is defined for this combination of argument types.
Closest candidates are:
add(!Matched::Integer, ::Integer)
@ Main.var"workspace#3" ~/work/course/course/probprog/Intro to Julia.jl#==#08b24136-c292-4360-a90e-a8fd82d45d6b:1
Stacktrace:
[1] macro expansion
@ ~/work/course/course/probprog/Intro to Julia.jl#==#0e341cb6-bbca-4581-858f-50b4e2ca858a:1 [inlined]mime'application/vnd.pluto.stacktrace+objectrootassigneelast_run_timestampA}*FA?persist_js_state·has_pluto_hook_features§cell_id$0e341cb6-bbca-4581-858f-50b4e2ca858adepends_on_disabled_cells§runtimepublished_object_keysdepends_on_skipped_cells§errored$54662c5d-7ba3-4e96-88ce-3c9ba1907f8equeued¤logsrunning¦outputbody7
For example, the cell below contains a mistake and evaluating it will throw an error. But which line has the mistake? Press the Show stack trace... button or Show more... to see the stack trace of the error below. Where did the error happen?
A matrix can be transposed by a single parenthesis, A'. Note that this does not mutate the array in memory. It just tells functions defined for matrices that it should change how it indexes the matrix's elements.
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[90m[14a3606d] [39m[93m↑ MozillaCACerts_jll v2025.5.20 ⇒ v2025.11.4[39m
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[90m[3f19e933] [39m[93m↑ p7zip_jll v17.5.0+2 ⇒ v17.7.0+0[39m
[0m[1mInstantiating...[22m
[90m===[39m
[0m[1mPrecompiling...[22m
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BmlipTeachingTools
[0m[1mResolving...[22m
[90m===[39m
[32m[1m Installed[22m[39m StableRNGs ─ v1.0.4
[36m[1m Project[22m[39m No packages added to or removed from `~/.julia/scratchspaces/c3e4b0f8-55cb-11ea-2926-15256bba5781/pkg_envs/env_ldphrmybhh/Project.toml`
[32m[1m Updating[22m[39m `~/.julia/scratchspaces/c3e4b0f8-55cb-11ea-2926-15256bba5781/pkg_envs/env_ldphrmybhh/Manifest.toml`
[90m[f43a241f] [39m[93m↑ Downloads v1.6.0 ⇒ v1.7.0[39m
[90m[44cfe95a] [39m[93m↑ Pkg v1.12.0 ⇒ v1.12.1[39m
[90m[deac9b47] [39m[93m↑ LibCURL_jll v8.11.1+1 ⇒ v8.15.0+0[39m
[90m[14a3606d] [39m[93m↑ MozillaCACerts_jll v2025.5.20 ⇒ v2025.11.4[39m
[90m[458c3c95] [39m[93m↑ OpenSSL_jll v3.5.1+0 ⇒ v3.5.4+0[39m
[90m[3f19e933] [39m[93m↑ p7zip_jll v17.5.0+2 ⇒ v17.7.0+0[39m
[0m[1mInstantiating...[22m
[90m===[39m
[0m[1mPrecompiling...[22m
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DataFrames
[0m[1mResolving...[22m
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[32m[1m Installed[22m[39m StableRNGs ─ v1.0.4
[36m[1m Project[22m[39m No packages added to or removed from `~/.julia/scratchspaces/c3e4b0f8-55cb-11ea-2926-15256bba5781/pkg_envs/env_ldphrmybhh/Project.toml`
[32m[1m Updating[22m[39m `~/.julia/scratchspaces/c3e4b0f8-55cb-11ea-2926-15256bba5781/pkg_envs/env_ldphrmybhh/Manifest.toml`
[90m[f43a241f] [39m[93m↑ Downloads v1.6.0 ⇒ v1.7.0[39m
[90m[44cfe95a] [39m[93m↑ Pkg v1.12.0 ⇒ v1.12.1[39m
[90m[deac9b47] [39m[93m↑ LibCURL_jll v8.11.1+1 ⇒ v8.15.0+0[39m
[90m[14a3606d] [39m[93m↑ MozillaCACerts_jll v2025.5.20 ⇒ v2025.11.4[39m
[90m[458c3c95] [39m[93m↑ OpenSSL_jll v3.5.1+0 ⇒ v3.5.4+0[39m
[90m[3f19e933] [39m[93m↑ p7zip_jll v17.5.0+2 ⇒ v17.7.0+0[39m
[0m[1mInstantiating...[22m
[90m===[39m
[0m[1mPrecompiling...[22m
[90m===[39m
ProgressMeter
[0m[1mResolving...[22m
[90m===[39m
[32m[1m Installed[22m[39m StableRNGs ─ v1.0.4
[36m[1m Project[22m[39m No packages added to or removed from `~/.julia/scratchspaces/c3e4b0f8-55cb-11ea-2926-15256bba5781/pkg_envs/env_ldphrmybhh/Project.toml`
[32m[1m Updating[22m[39m `~/.julia/scratchspaces/c3e4b0f8-55cb-11ea-2926-15256bba5781/pkg_envs/env_ldphrmybhh/Manifest.toml`
[90m[f43a241f] [39m[93m↑ Downloads v1.6.0 ⇒ v1.7.0[39m
[90m[44cfe95a] [39m[93m↑ Pkg v1.12.0 ⇒ v1.12.1[39m
[90m[deac9b47] [39m[93m↑ LibCURL_jll v8.11.1+1 ⇒ v8.15.0+0[39m
[90m[14a3606d] [39m[93m↑ MozillaCACerts_jll v2025.5.20 ⇒ v2025.11.4[39m
[90m[458c3c95] [39m[93m↑ OpenSSL_jll v3.5.1+0 ⇒ v3.5.4+0[39m
[90m[3f19e933] [39m[93m↑ p7zip_jll v17.5.0+2 ⇒ v17.7.0+0[39m
[0m[1mInstantiating...[22m
[90m===[39m
[0m[1mPrecompiling...[22m
[90m===[39m
enabled÷restart_recommended_msgrestart_required_msgbusy_packageswaiting_for_permission,waiting_for_permission_but_probably_disabled«cell_inputs g$122a00c1-d3d4-43da-b5d1-6bc660f5d43ecell_id$122a00c1-d3d4-43da-b5d1-6bc660f5d43ecodemmd"""
If you need both the index and the value of the array element, you can use the `enumerate` command:
"""metadatashow_logsèdisabled®skip_as_script«code_folded$f72045aa-fa31-40bf-b80c-5259583f1d30cell_id$f72045aa-fa31-40bf-b80c-5259583f1d30code\md"""
You will see much more of the `Distributions.jl` package in this course. See also:
"""metadatashow_logsèdisabled®skip_as_script«code_folded$ccbf4589-8d25-434e-a7f4-3d972b4ee078cell_id$ccbf4589-8d25-434e-a7f4-3d972b4ee078codew = [1 2 3 4]metadatashow_logsèdisabled®skip_as_script«code_folded$3889c64c-d018-4c04-80a4-246aaede7d4ecell_id$3889c64c-d018-4c04-80a4-246aaede7d4ecode٫begin
function foo(bar::Float64)
message = "Boo!"
return message
end
function foo(bar::Integer)
message = "Bah!"
return message
end
foo(1)
endmetadatashow_logsèdisabled®skip_as_script«code_folded$dab1a565-43a9-48ac-896f-cc0ee7856552cell_id$dab1a565-43a9-48ac-896f-cc0ee7856552code md"""
## Packages
The base form of Julia has many wonderful functions and methods. But not everything. To extend functionality, we have to import additional software packages. Below is a list of the few packages we cover in today's tutorial. But you'll see more later in the course.
"""metadatashow_logsèdisabled®skip_as_script«code_folded$28f3894f-6135-4359-842e-ef5e783fc469cell_id$28f3894f-6135-4359-842e-ef5e783fc469codemd"""
## Errors & Debugging
- References: [Stack traces](https://docs.julialang.org/en/v1/manual/stacktraces/)
When you call a function that Julia doesn't know, it will return a list of the steps it took to execute your command and point to where its progress was blocked. This is highly useful but it typically requires a bit of practice to parse (i.e., read and filter) stack traces.
### MethodError
Suppose we write a function that expects an `Integer` input and call that function with an `Float64` argument:
"""metadatashow_logsèdisabled®skip_as_script«code_folded$f77783b5-b35a-4437-b436-323d7668d456cell_id$f77783b5-b35a-4437-b436-323d7668d456codecmd"""
It is possible to add plots to the same figure by using a `!` added to your plot command.
"""metadatashow_logsèdisabled®skip_as_script«code_folded$8d64ec48-639e-4fc2-9c6c-5cd207c1ba75cell_id$8d64ec48-639e-4fc2-9c6c-5cd207c1ba75codeadd1(3)metadatashow_logsèdisabled®skip_as_script«code_folded$6bb76a54-2df8-4604-923a-ebb428eb0353cell_id$6bb76a54-2df8-4604-923a-ebb428eb0353code٠md"""
They can be concatenated by multiplication (which is an example of a function, namely `*`, which acts differently on different input argument types):
"""metadatashow_logsèdisabled®skip_as_script«code_folded$25c4102b-9ed9-44c7-9c5f-9d7e1810f229cell_id$25c4102b-9ed9-44c7-9c5f-9d7e1810f229code%begin
e = [1, 3, 2]
[sort(e) e]
endmetadatashow_logsèdisabled®skip_as_script«code_folded$28c7a5ed-cbc7-4865-a6a9-b6395ea80a5ccell_id$28c7a5ed-cbc7-4865-a6a9-b6395ea80a5ccode[md"""
### Stack trace
The stack trace will show you exactly _where_ an error happened.
"""metadatashow_logsèdisabled®skip_as_script«code_folded$ec16be17-cdbd-467a-be07-a6fed4e05dadcell_id$ec16be17-cdbd-467a-be07-a6fed4e05dadcodemd"""
Julia also has a `Symbol` type, which is used for [meta-programming](https://docs.julialang.org/en/v1/manual/metaprogramming/) (not important for this course). A `Symbol` type is characterized by a `:` in front of a word. For example:
"""metadatashow_logsèdisabled®skip_as_script«code_folded$77271b72-bafe-11f0-8fa2-33da6741b124cell_id$77271b72-bafe-11f0-8fa2-33da6741b124codemd"""
This notebook will teach you some of the basic programming routines in Julia. You will need these skills to complete the probabilistic programming assignments later on in the course. We will assume basic familiarity with programming, such as for-loops, if-else statements and function definitions.
Resources:
- **Julia Basics** from _"Julia Programming for Machine Learning"_ taught at TU Berlin:
- [L1: Essentials](https://adrianhill.de/julia-ml-course/L1_Basics_1/) (syntax, types, operations, functions)
- [L2: Arrays](https://adrianhill.de/julia-ml-course/L2_Basics_2/) (vector, matrix, linear algebra)
- [JuliaLang documentation](https://docs.julialang.org/en/v1/)
- [Differences to Python, Matlab, C and Java](https://docs.julialang.org/en/v1/manual/noteworthy-differences/)
- [Video on getting started](https://www.youtube.com/watch?v=4igzy3bGVkQ&list=PLP8iPy9hna6SCcFv3FvY_qjAmtTsNYHQE)
- [Pluto.jl documentation](https://plutojl.org/en/docs/)
"""metadatashow_logsèdisabled®skip_as_script«code_folded$73a811a3-8c64-4bf0-9656-1d8488819f45cell_id$73a811a3-8c64-4bf0-9656-1d8488819f45code٥md"""
Macros are a somewhat advanced form of metaprogramming. You will not need to define any new macros; this instruction is just here to explain what they are.
"""metadatashow_logsèdisabled®skip_as_script«code_folded$70a9cd5f-ec47-4c45-b822-64c3ff72322acell_id$70a9cd5f-ec47-4c45-b822-64c3ff72322acodeeigen([3. 2.;2. 0.4])metadatashow_logsèdisabled®skip_as_script«code_folded$63530cf1-e20d-4250-a6e0-68443253a0e7cell_id$63530cf1-e20d-4250-a6e0-68443253a0e7codecscatter(X[:,1], X[:,2],
xlabel="X_1",
ylabel="X_2",
markersize=10,
markershape=:circle)metadatashow_logsèdisabled®skip_as_script«code_folded$400ad142-8fad-42f6-a8cb-3a1b9c56f5dbcell_id$400ad142-8fad-42f6-a8cb-3a1b9c56f5dbcode md"""
## Closing
That's it for now. If you encounter mysterious errors, please let us know on [Piazza](https://piazza.com/tue.nl/winter2026/5ssd0). We can add them to this primer.
And if you have any feedback about improving this short primer on programming in Julia, let us know!
"""metadatashow_logsèdisabled®skip_as_script«code_folded$4588df60-9c5b-49cc-a3a1-44db790d00edcell_id$4588df60-9c5b-49cc-a3a1-44db790d00edcode0md"""
## Pluto notebooks
The course is built in Pluto.jl, a reactive programming environment. Pluto notebooks are wonderfully intuitive and interactive, and are already revolutionizing mathematics and computer science education (e.g., [18.S191 Computational Thinking @MIT](https://computationalthinking.mit.edu)).
A few things to be aware of when working in Pluto notebooks:
- Code is not executed sequentially. In other words, you can call a variable in a cell even if that variable is defined in a later cell.
- You cannot re-use variable names, i.e., you cannot overwrite a variable with a different variable in a latter cell.
- A cell can only execute a single function/instruction; if you want to execute more instructions, you have to wrap them in a `begin .. end` environment.
- Each Pluto notebook manages its own software packages (more on that later).
- The `Live docs` button on the bottom-right corner can be used to look up documentation of functions.
- The `Status` button on the bottom-right corner displays what the kernel is doing in the background.
"""metadatashow_logsèdisabled®skip_as_script«code_folded$a5a577b6-4266-4698-a3a1-7147590795b5cell_id$a5a577b6-4266-4698-a3a1-7147590795b5code
md"""
Note that the `return` argument does not need to be at the end of a function ([the return keyword](https://docs.julialang.org/en/v1/manual/functions/#The-return-Keyword)).
You don't actually need the `function` keyword if you have simple enough functions:
"""metadatashow_logsèdisabled®skip_as_script«code_folded$ecea873a-ab10-4539-ba66-b05b1ebdf1eccell_id$ecea873a-ab10-4539-ba66-b05b1ebdf1eccodemd"""
You will not have to use `Symbol`s in the course, but you may see one every once in a while in the lecture notes. For example, the `plot` command (see Visualization section), may have a `markershape=:cross` argument.
"""metadatashow_logsèdisabled®skip_as_script«code_folded$cf9d6290-0aeb-484a-8816-6972fd3c4891cell_id$cf9d6290-0aeb-484a-8816-6972fd3c4891codesin.([1., 2., 3.])metadatashow_logsèdisabled®skip_as_script«code_folded$e500c93a-9a4a-4141-819b-051c4e5d5bb0cell_id$e500c93a-9a4a-4141-819b-051c4e5d5bb0code5md"""
Here is the function used in the last cell:
"""metadatashow_logsèdisabled®skip_as_script«code_folded$755d9324-5447-4240-9a17-6e212dab4eddcell_id$755d9324-5447-4240-9a17-6e212dab4eddcodeCmd"""
`plot` and `scatter` are the most useful commands. A `scatter` command will ignore properties such as `linewidth` and `linestyle` (since there are no lines) and will listen to `markersize` and `markershape` commands (see [Supported Attributes](https://docs.juliaplots.org/stable/generated/supported/) in the API).
"""metadatashow_logsèdisabled®skip_as_script«code_folded$3d89c37f-0876-4ba1-aa35-0a7273d4d269cell_id$3d89c37f-0876-4ba1-aa35-0a7273d4d269codev = [1,2,3,4]metadatashow_logsèdisabled®skip_as_script«code_folded$794970ef-f2d2-4dc8-ae43-2b1ecc306a74cell_id$794970ef-f2d2-4dc8-ae43-2b1ecc306a74codegive_magic_number(7)metadatashow_logsèdisabled®skip_as_script«code_folded$5905847d-2358-4380-a5a0-c5ac8c716839cell_id$5905847d-2358-4380-a5a0-c5ac8c716839code.begin
px = Normal(1.0, 0.5)
pdf(px, 0.0)
endmetadatashow_logsèdisabled®skip_as_script«code_folded$277c5574-910b-4f05-8661-ef81278e9319cell_id$277c5574-910b-4f05-8661-ef81278e9319codeVmd"""
## Control flow
- References: [Control flow](https://docs.julialang.org/en/v1/manual/control-flow/), [Logical Operators](https://docs.julialang.org/en/v1/manual/missing/#Logical-operators)
Control flow refers to redirecting how a compiler goes through a program. Instead of traversing it line-by-line, things like `if-else` statements can make a compiler skip steps. These require logical operations: you can use `==` to check if two variables have the same value, `===` to check if they are actually the same object (i.e., same memory reference) and `!=` to check if they're not equal.
"""metadatashow_logsèdisabled®skip_as_script«code_folded$ce73c7c3-5025-4784-8657-b2b67097c702cell_id$ce73c7c3-5025-4784-8657-b2b67097c702codeCmd"""
## Functions
- References: [Functions](https://docs.julialang.org/en/v1/manual/functions/), [Mutation](https://docs.julialang.org/en/v1/manual/style-guide/#bang-convention)
Function and expressions are a core component of the julia language. Its "multiple dispatch" feature means that you can define multiple functions with the same name but with behaviour that depends on the input argument types. When you're starting out, you may not notice this so much, but you will start to appreciate this feature tremendously when you begin to professionally develop software.
"""metadatashow_logsèdisabled®skip_as_script«code_folded$f5d8574f-b115-4555-8c0e-41f95824740acell_id$f5d8574f-b115-4555-8c0e-41f95824740acodetypeof(d)metadatashow_logsèdisabled®skip_as_script«code_folded$d5a8ec92-a4fa-46e6-983c-44572a74f886cell_id$d5a8ec92-a4fa-46e6-983c-44572a74f886codeفbegin
using BmlipTeachingTools
using LinearAlgebra
using DataFrames
using ProgressMeter
using Distributions
using Plots
endmetadatashow_logsèdisabled®skip_as_script«code_folded$9dc43526-5604-4251-aa22-3aff5fa3bd0bcell_id$9dc43526-5604-4251-aa22-3aff5fa3bd0bcode#fn(; number::Number = 1) = 1/numbermetadatashow_logsèdisabled®skip_as_script«code_folded$705dedd6-755f-4a18-9d4d-cde8c9755e05cell_id$705dedd6-755f-4a18-9d4d-cde8c9755e05codeTableOfContents()metadatashow_logsèdisabled®skip_as_script«code_folded$034f3378-6dc8-4fff-b8a7-afdc330b4f01cell_id$034f3378-6dc8-4fff-b8a7-afdc330b4f01code:for (j,n) in enumerate(range(0,3))
@info("$j, $n")
endmetadatashow_logsèdisabled®skip_as_script«code_folded$61f5260a-dd5b-4ca1-9d55-30d7fd453f4ecell_id$61f5260a-dd5b-4ca1-9d55-30d7fd453f4ecodeebegin
r = 3.0
if r < 0
"Negative"
elseif r == 0
"0.0"
else
"Positive"
end
endmetadatashow_logsèdisabled®skip_as_script«code_folded$83e2a97e-72d7-404e-b138-f2c5d30d6365cell_id$83e2a97e-72d7-404e-b138-f2c5d30d6365codeab = "a"*"b"metadatashow_logsèdisabled®skip_as_script«code_folded$cc21a0ab-d413-453b-94a0-15d33524ca4fcell_id$cc21a0ab-d413-453b-94a0-15d33524ca4fcodefor n = 1:2:5
@info(n)
endmetadatashow_logsèdisabled®skip_as_script«code_folded$8fe19ca9-6618-4c70-8eca-6ba002630ca9cell_id$8fe19ca9-6618-4c70-8eca-6ba002630ca9codeadd(3,4)metadatashow_logsèdisabled®skip_as_script«code_folded$408e3447-21bb-4617-bdf2-d60f7cfb8ececell_id$408e3447-21bb-4617-bdf2-d60f7cfb8ececodeumd"""
You may be familiar with "list comprehension", which is a shortened form of iterating through a collection:
"""metadatashow_logsèdisabled®skip_as_script«code_folded$e608d8a8-8faa-4302-bf7e-ae135cef47a4cell_id$e608d8a8-8faa-4302-bf7e-ae135cef47a4codetypeof(c)metadatashow_logsèdisabled®skip_as_script«code_folded$e47bad96-4092-4d0a-8035-f05310359565cell_id$e47bad96-4092-4d0a-8035-f05310359565codemd"""
## Broadcasting
- Reference: [Broadcasting](https://docs.julialang.org/en/v1/manual/arrays/#Broadcasting)
You can apply functions to elements in an array by placing a dot in front:
"""metadatashow_logsèdisabled®skip_as_script«code_folded$f5df9bc3-79df-4e0b-b199-9ade76f53894cell_id$f5df9bc3-79df-4e0b-b199-9ade76f53894codetypeof(a)metadatashow_logsèdisabled®skip_as_script«code_folded$be6f2317-24c7-470c-bde8-233ad3d6f3bdcell_id$be6f2317-24c7-470c-bde8-233ad3d6f3bdcodeHbegin
A = [3 2 1;
2 3 2;
1 2 3]
x = [0,
1,
2]
A*x
endmetadatashow_logsèdisabled®skip_as_script«code_folded$767a5b82-b007-42aa-897c-6dfa4eadf28acell_id$767a5b82-b007-42aa-897c-6dfa4eadf28acode.md"""
This also works for named functions:
"""metadatashow_logsèdisabled®skip_as_script«code_folded$58b280bc-914e-45e2-bae4-3c767ba09ec3cell_id$58b280bc-914e-45e2-bae4-3c767ba09ec3codeSmd"""
Matrix operations are intuitive and similar to the mathematical notation:
"""metadatashow_logsèdisabled®skip_as_script«code_folded$a02297a2-8660-4fd1-95af-438f363b9f29cell_id$a02297a2-8660-4fd1-95af-438f363b9f29code["n = $n" for n in range(2,4)]metadatashow_logsèdisabled®skip_as_script«code_folded$02c03dad-d974-4584-9766-0e7ea79047e0cell_id$02c03dad-d974-4584-9766-0e7ea79047e0codemd"""
## Data types
- References: [Numbers](https://docs.julialang.org/en/v1/manual/integers-and-floating-point-numbers/), [Integers and Float](https://docs.julialang.org/en/v1/manual/integers-and-floating-point-numbers/), [Strings](https://docs.julialang.org/en/v1/base/strings/), [Symbols](https://docs.julialang.org/en/v1/manual/metaprogramming/).
Numbers in Julia have specific types, most notably `Integer`, `Real` and `Complex`. (See [this documentation page](https://docs.julialang.org/en/v1/base/numbers/) for the full type tree.) It is important to be aware of what type your numbers are because many functions operate differently on different number types.
"""metadatashow_logsèdisabled®skip_as_script«code_folded$721d9bd7-c04c-4874-897e-61fde49ba257cell_id$721d9bd7-c04c-4874-897e-61fde49ba257codefn(x::Number) = 1/xmetadatashow_logsèdisabled®skip_as_script«code_folded$14e2c87f-557e-45fa-8036-464d5b4deac5cell_id$14e2c87f-557e-45fa-8036-464d5b4deac5codeumd"""
You should read this as "there exists a function called `add1` that expects an `Integer` input." Try that.
"""metadatashow_logsèdisabled®skip_as_script«code_folded$3e1ca65e-f4cc-4d28-8139-f04d70980ecbcell_id$3e1ca65e-f4cc-4d28-8139-f04d70980ecbcodeb = 3.0metadatashow_logsèdisabled®skip_as_script«code_folded$e5555433-b323-4af5-805c-db592461307bcell_id$e5555433-b323-4af5-805c-db592461307bcode/md"""
#### Mathced types in MethodError
The red highlighting of $(html"::Integer") is also important but requires a slightly more complicated example. Suppose we have a function with two `Integer` inputs and we call with `Float64` and `Int64` arguments.
"""metadatashow_logsèdisabled®skip_as_script«code_folded$881a67da-5f59-437d-91ce-8c8113985fb6cell_id$881a67da-5f59-437d-91ce-8c8113985fb6code9begin
U = zeros(2,3)
V = ones(2,3)
W = randn(2,3)
end;metadatashow_logsèdisabled®skip_as_script«code_folded$b6399549-c754-498a-887c-401f252ba21fcell_id$b6399549-c754-498a-887c-401f252ba21fcodeTfunction give_magic_number(x::Real)
kk = x*2
ll = 3*kk
mm = kl*ll
nn = mm*ll
endmetadatashow_logsèdisabled®skip_as_script«code_folded$90d21b8f-b29b-420c-894b-a94abb52f2bbcell_id$90d21b8f-b29b-420c-894b-a94abb52f2bbcodefn(4)metadatashow_logsèdisabled®skip_as_script«code_folded$9d9799b0-2e0c-4180-ae80-44e5c268c8b4cell_id$9d9799b0-2e0c-4180-ae80-44e5c268c8b4codea = 3metadatashow_logsèdisabled®skip_as_script«code_folded$9f761389-7125-4df0-877f-9925b315913fcell_id$9f761389-7125-4df0-877f-9925b315913fcode^md"""
Below are some examples of importing packages and using their added functionalities.
"""metadatashow_logsèdisabled®skip_as_script«code_folded$897d515d-bfda-4a8f-abbb-9276d69f0f4dcell_id$897d515d-bfda-4a8f-abbb-9276d69f0f4dcodeadd1(3.1415)metadatashow_logsèdisabled®skip_as_script«code_folded$ebbf4498-4082-44a0-a904-c80ca6dab2c7cell_id$ebbf4498-4082-44a0-a904-c80ca6dab2c7code[fn() fn(number=3)]metadatashow_logsèdisabled®skip_as_script«code_folded$2bad907d-5859-4465-8ed6-4285642d9874cell_id$2bad907d-5859-4465-8ed6-4285642d9874codeHmd"""
Note that we first of all get a `MethodError`. This points to the fact that Julia could not find the function (i.e, method) that you asked for; `add1(::Float64)` does not exist.
Furthermore, Julia provides a list of "Closest candidates" which are functions of the same name with different input arguments. It reports:
"""metadatashow_logsèdisabled®skip_as_script«code_folded$660571c4-3d5e-4eba-b6d9-bcab17c2a2eecell_id$660571c4-3d5e-4eba-b6d9-bcab17c2a2eecodetitle("Programming in Julia")metadatashow_logsèdisabled®skip_as_script«code_folded$4f785723-2f6a-4dcd-82a7-8d15daf191e8cell_id$4f785723-2f6a-4dcd-82a7-8d15daf191e8codemd"""
### What to do with errors?
To summarize, when you get an error, it is important to **take your time**, and **read the message**. If you want to know _where_ something happened, look at the stack trace. Try to see an error message as **positive feedback**: you are on the right track, and Julia is trying to help you to write the correct code.
The type of error can also be informative. The `MethodError` is probably the error you will see most often.
"""metadatashow_logsèdisabled®skip_as_script«code_folded$51123db8-3fdf-4497-b121-ce5b989bc063cell_id$51123db8-3fdf-4497-b121-ce5b989bc063codeFmd"""
You can incorporate numbers into strings through a `$` call:
"""metadatashow_logsèdisabled®skip_as_script«code_folded$c66b8dec-aa58-4508-9f93-70d65ba2c051cell_id$c66b8dec-aa58-4508-9f93-70d65ba2c051codexmd"""
We again get the `MethodError` that the function we asked for doesn't exist and a suggested alternative (i.e., "closest candidate"). But this time, only the first argument $(html"::Integer") is highlighted in red.
Julia checks your input argument types against those in the closest candidates. This tells you _what_ to change: the solution would be to either:
- Change the call: Make the first argument of your function call to an `Integer` type. That would be `add(3, 4)`.
- Change the defintion: Make the function accept a more general `Real` number as the first argument.
"""metadatashow_logsèdisabled®skip_as_script«code_folded$895960bf-1ee2-4aa8-b38c-5857525b1ddccell_id$895960bf-1ee2-4aa8-b38c-5857525b1ddccode`md"""
Matrices can be constructed by separating elements with spaces and rows by semicolons:
"""metadatashow_logsèdisabled®skip_as_script«code_folded$08b24136-c292-4360-a90e-a8fd82d45d6bcell_id$08b24136-c292-4360-a90e-a8fd82d45d6bcode9function add(a::Integer, b::Integer)
return a + b
endmetadatashow_logsèdisabled®skip_as_script«code_folded$e3be7db2-a307-4083-bb35-db4e70dfe1bfcell_id$e3be7db2-a307-4083-bb35-db4e70dfe1bfcodemd"""
## Visualization
- Reference: [Plots.jl](https://github.com/JuliaPlots/Plots.jl)
Plots.jl provides a common interface to call various other visualization backends (GR, Matplotlib, PGFPlotsX, Plotly, etc.). In other words, commands like `plot(..)` will be translated into the appropriate command for the backend. So, it does not re-invent the wheel but rather gives you access to the already enormous field of visualization tools.
Below are a few examples of the most common visualization commands you'll see throughout the course. The core principle is to use a `plot` type as base command and then provide keyword arguments (in `String`, `Number` or `Symbol` type) to apply variations.
"""metadatashow_logsèdisabled®skip_as_script«code_folded$3b0e1194-e6df-46e4-8c41-032f5beeb8facell_id$3b0e1194-e6df-46e4-8c41-032f5beeb8facodeemd"""
You can add keyword arguments to a function, which are input arguments with default values:
"""metadatashow_logsèdisabled®skip_as_script«code_folded$7bc7fb04-9d74-4970-b06b-5bc95d7be757cell_id$7bc7fb04-9d74-4970-b06b-5bc95d7be757codeQmd"""
Strings are constructed by enclosing symbols within double parentheses.
"""metadatashow_logsèdisabled®skip_as_script«code_folded$6b4c2d62-b1d0-4f42-9ee6-eb2d9f8ba98acell_id$6b4c2d62-b1d0-4f42-9ee6-eb2d9f8ba98acodetypeof(b)metadatashow_logsèdisabled®skip_as_script«code_folded$826ef035-bf26-45ac-b33c-dc2dcaa23f7ccell_id$826ef035-bf26-45ac-b33c-dc2dcaa23f7ccode#r > 0 ? "Positive" : "Not positive"metadatashow_logsèdisabled®skip_as_script«code_folded$909a83f1-507c-4d8f-855e-f1a45d3aa927cell_id$909a83f1-507c-4d8f-855e-f1a45d3aa927code'begin
plot(xx, pdf.(Normal(0.,1.), xx),
xlabel="x",
ylabel="p(x)",
label="N(0,1)",
color="red",
linewidth=5,
linestyle=:dash)
plot!(xx, pdf.(Normal(1.,0.5), xx),
xlabel="x",
ylabel="p(x)",
label="N(1,0.5)",
color="blue",
linestyle=:solid)
endmetadatashow_logsèdisabled®skip_as_script«code_folded$de01ba69-cc44-4f3a-8dfa-98f4a194b28acell_id$de01ba69-cc44-4f3a-8dfa-98f4a194b28acode9md"""
## Macros
- References: [Macros](https://docs.julialang.org/en/v1/manual/metaprogramming/#man-macros)
Words that start with the `@` symbol are _macros_ in Julia, for example `@time, @test, @model`. They represent a series of functions called on an input structure and are really handy when you have to use the same set of instructions often.
For example, you could define a `ProgressMeter` bar, update it at every iteration of a for-loop and write a custom print statement every time. _Or_, you could call the `@showprogress` macro on the for-loop itself:
"""metadatashow_logsèdisabled®skip_as_script«code_folded$6969d1e5-38d0-432d-842e-153139f86613cell_id$6969d1e5-38d0-432d-842e-153139f86613code"e = $a"metadatashow_logsèdisabled®skip_as_script«code_folded$5013d835-99b7-4b08-bc97-8085017d47abcell_id$5013d835-99b7-4b08-bc97-8085017d47abcoded = "3"metadatashow_logsèdisabled®skip_as_script«code_folded$ab9f639a-abd0-44e0-bb89-ed27472a641dcell_id$ab9f639a-abd0-44e0-bb89-ed27472a641dcode 3 .*[1 2 3]metadatashow_logsèdisabled®skip_as_script«code_folded$2f5ff4dc-5267-4d64-aca5-a6a0be536f8fcell_id$2f5ff4dc-5267-4d64-aca5-a6a0be536f8fcode4for n in range(0, stop=4, length=2)
@info(n)
endmetadatashow_logsèdisabled®skip_as_script«code_folded$8ebd00be-c361-4080-b1a6-8eca643439a5cell_id$8ebd00be-c361-4080-b1a6-8eca643439a5codetypeof(f)metadatashow_logsèdisabled®skip_as_script«code_folded$174612aa-d8a0-4a21-be83-91648dac1f61cell_id$174612aa-d8a0-4a21-be83-91648dac1f61codex'*A*xmetadatashow_logsèdisabled®skip_as_script«code_folded$113fa658-4325-4ea6-a5ab-6337889006f4cell_id$113fa658-4325-4ea6-a5ab-6337889006f4code.function add1(a::Integer)
return a + 1
endmetadatashow_logsèdisabled®skip_as_script«code_folded$a520e936-d80b-42fe-9b45-28d972383ff9cell_id$a520e936-d80b-42fe-9b45-28d972383ff9code}md"""
But if I call the `sort!` function and the original vector, you'll see that the original vector is now also sorted.
"""metadatashow_logsèdisabled®skip_as_script«code_folded$0103d1f6-ea03-4497-a0de-e1b0c181d648cell_id$0103d1f6-ea03-4497-a0de-e1b0c181d648codemetadatashow_logsèdisabled®skip_as_script«code_folded$5e402035-3a17-4072-8288-cbc613bc4cbacell_id$5e402035-3a17-4072-8288-cbc613bc4cbacoden@htl """
Closest candidates are:
add1(::Integer)
"""metadatashow_logsèdisabled®skip_as_script«code_folded$6048a5ad-2964-4aab-a708-32754e52eb1ccell_id$6048a5ad-2964-4aab-a708-32754e52eb1ccode{plot(xx, pdf.(px, xx),
xlabel="x",
ylabel="p(x)",
label="pdf",
color="red",
linewidth=5,
linestyle=:dash)metadatashow_logsèdisabled®skip_as_script«code_folded$d2d811d0-9e38-4fc6-b576-3156309b3715cell_id$d2d811d0-9e38-4fc6-b576-3156309b3715code"xx = range(-3, stop=3, length=301)metadatashow_logsèdisabled®skip_as_script«code_folded$66a29ea6-d467-4909-964d-c88d68da4d50cell_id$66a29ea6-d467-4909-964d-c88d68da4d50code3md"""
Simple `if-else` statements can often be replaced by `ternary` checks. Essentially, you ask a question (a logical operation followed by `?`) and then tell the program what to do when the answer is yes (written immediately after the question) or no (written after the yes-answer followed by a `:`).
"""metadatashow_logsèdisabled®skip_as_script«code_folded$44add801-211a-423d-9279-54ab6a101420cell_id$44add801-211a-423d-9279-54ab6a101420code,md"""
Functions that modify their input arguments instead of creating new output variables are typically marked with an `!`. Below I have defined an unsorted vector and I call `sort` to sort it in increasing order. If I call the sort function and the original vector, then they will be different:
"""metadatashow_logsèdisabled®skip_as_script«code_folded$bfbfe9cf-9a28-4b52-8c50-4ab9965a6288cell_id$bfbfe9cf-9a28-4b52-8c50-4ab9965a6288codeX = randn(10,2)metadatashow_logsèdisabled®skip_as_script«code_folded$29f6c7eb-69ba-4072-a77d-7097235c1daccell_id$29f6c7eb-69ba-4072-a77d-7097235c1daccodeٹmd"""
`Int64` is a 64-byte integer. Other options are 32-,16-, or 8-bit integers and they can be unsigned as well. The default real-valued numbers is a 64-bit floating-point number:
"""metadatashow_logsèdisabled®skip_as_script«code_folded$5d627a4e-5dee-4c25-b99c-ae7e4221109fcell_id$5d627a4e-5dee-4c25-b99c-ae7e4221109fcode*md"""
Converting number types is easy:
"""metadatashow_logsèdisabled®skip_as_script«code_folded$77f5b5de-040f-4406-bb57-c1fe58e3b32bcell_id$77f5b5de-040f-4406-bb57-c1fe58e3b32bcode7md"""
## Array manipulation
- References: [Arrays](https://docs.julialang.org/en/v1/base/arrays/)
Arrays are indexed with square brackets, `A[i,j]`. You can construct a matrix by enclosing a set of numbers with square brackets. If you separate your numbers with comma's, then you will get a column vector:
"""metadatashow_logsèdisabled®skip_as_script«code_folded$0e341cb6-bbca-4581-858f-50b4e2ca858acell_id$0e341cb6-bbca-4581-858f-50b4e2ca858acodeadd(3.0, 4)metadatashow_logsèdisabled®skip_as_script«code_folded$54662c5d-7ba3-4e96-88ce-3c9ba1907f8ecell_id$54662c5d-7ba3-4e96-88ce-3c9ba1907f8ecodemd"""
For example, the cell below contains a mistake and evaluating it will throw an error. But which line has the mistake? Press the **Show stack trace...** button or **Show more...** to see the stack trace of the error below. Where did the error happen?
"""metadatashow_logsèdisabled®skip_as_script«code_folded$7a1e8d0a-cffc-497a-88a7-fd9757bc8edacell_id$7a1e8d0a-cffc-497a-88a7-fd9757bc8edacodef = :foometadatashow_logsèdisabled®skip_as_script«code_folded$b3e11050-b799-4d88-b5cc-bc9d057be7bccell_id$b3e11050-b799-4d88-b5cc-bc9d057be7bccode.@showprogress for n in 1:10
sleep(0.2)
endmetadatashow_logsèdisabled®skip_as_script«code_folded$519dbc40-2c83-4fda-b6fe-d3547b43b407cell_id$519dbc40-2c83-4fda-b6fe-d3547b43b407code(md"""
Common array constructors are:
"""metadatashow_logsèdisabled®skip_as_script«code_folded$f4753dd6-51f7-48db-b8e9-26b550af1baccell_id$f4753dd6-51f7-48db-b8e9-26b550af1baccode[sort!(x) x]metadatashow_logsèdisabled®skip_as_script«code_folded$0d8059ae-c158-43f2-81a8-9cba2f667177cell_id$0d8059ae-c158-43f2-81a8-9cba2f667177codehmd"""
If you use spaces, then you will construct a row vector (i.e., a matrix of dimensions 1 by n):
"""metadatashow_logsèdisabled®skip_as_script«code_folded$c97780c0-c60f-443d-98c8-100e67576e23cell_id$c97780c0-c60f-443d-98c8-100e67576e23codemd"""
A matrix can be transposed by a single parenthesis, `A'`. Note that this does not mutate the array in memory. It just tells functions defined for matrices that it should change how it indexes the matrix's elements.
"""metadatashow_logsèdisabled®skip_as_script«code_folded$8a606467-0434-418f-85e5-40a35c9df95fcell_id$8a606467-0434-418f-85e5-40a35c9df95fcodeXbegin
D = Dict(
"a" => 1,
"b" => 2,
"c" => 3
)
df = DataFrame(D)
endmetadatashow_logsèdisabled®skip_as_script«code_folded$ff063276-46ef-4768-a0b1-878e9eb1a13ecell_id$ff063276-46ef-4768-a0b1-878e9eb1a13ecodeّmd"""
Next, we can use the `range` command to construct an array of numbers and then use the `in` command to loop over elements in the array:
"""metadatashow_logsèdisabled®skip_as_script«code_folded$96b831a8-09ba-4792-8268-14c368b804f8cell_id$96b831a8-09ba-4792-8268-14c368b804f8codeM = [1 2; 3 4]metadatashow_logsèdisabled®skip_as_script«code_folded$2e3b7a55-a85b-4498-8dc4-c14853ec06abcell_id$2e3b7a55-a85b-4498-8dc4-c14853ec06abcodemd"""
## Iteration
- Reference: [Collections](https://docs.julialang.org/en/v1/base/collections/)
For-loops are one of the simplest forms of iteration and can be defined in a number of ways. First, the matlab way:
"""metadatashow_logsèdisabled®skip_as_script«code_folded$14ab0808-3fdb-4113-8854-43255987a006cell_id$14ab0808-3fdb-4113-8854-43255987a006codec = convert(Float64, 3)metadatashow_logsèdisabled®skip_as_script«code_folded$eacafc14-d0f6-472f-be69-2ab0d81e41b1cell_id$eacafc14-d0f6-472f-be69-2ab0d81e41b1codeTNotebookCard("https://bmlip.github.io/course/minis/Distributions%20in%20Julia.html")metadatashow_logsèdisabled®skip_as_script«code_foldedënotebook_id$6c521516-4560-11f1-9991-1b1093306814in_temp_dir¨metadata
