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_quarto.yml
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@ -47,6 +47,8 @@ website:
text: "📝 3 - First Steps: Handout"
- href: "material/1_mon/firststeps/tasks.qmd"
text: "🛠 3 - First Steps: Exercises"
- href: "https://github.com/s-ccs/summerschool_simtech_2023/blob/main/material/1_mon/firststeps/statistic_functions.jl"
text: "✔ 3 - Solutions"
- href: "material/1_mon/envs/envs_handout.qmd"
text: "📝 4 - Envs & Pkgs : Handout"
- href: "material/1_mon/envs/tasks.qmd"
@ -57,9 +59,9 @@ website:
text: "📝 1 - Advanced Git and Contributing"
- href: "material/2_tue/git/tasks.qmd"
text: "🛠 1 - Git: Exercises"
- href: "material/2_tue/testing/slides.qmd"
- href: "material/2_tue/testing/slides.md"
text: "📝 2 - Testing"
- href: "material/2_tue/CI/missing.qmd"
- href: "material/2_tue/ci/slides.md"
text: "📝 3 - Continuous Integration"
- href: material/2_tue/codereview/slides.qmd
text: "📝 4 - Code Review"

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cheatsheets/git.qmd
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There are many good ones out there. One we can recommend is the [one from GitHub](https://education.github.com/git-cheat-sheet-education.pdf).

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cheatsheets/githubactions.qmd
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Also [one from GitHub](https://github.github.io/actions-cheat-sheet/actions-cheat-sheet.pdf)

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index.qmd
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@ -22,6 +22,9 @@ Seminar room in the groundfloor (directly at the entrance)
[Link to map](https://www.simtech.uni-stuttgart.de/events/simtech-summer-school/SuSch_2/location/)
#### ⚗ Advanced topics
We probably have some time to discuss advanced topics towards the end of the summers school. You are welcome to send an email to benedikt and/or put it into [the git issue](https://github.com/s-ccs/summerschool_simtech_2023/issues/15)
----
We wish you all a interesting, safe and fun summerschool. If there are any interpersonal issues (especially regarding [code-of-conduct](https://www.uni-stuttgart.de/en/university/profile/diversity/code-of-conduct/)), please directly contact [Benedikt Ehinger](benedikt.ehinger@vis.uni-stuttgart.de)^[If there are problem with him, please contact **Marco Oesting**]. For organizational issues, please contact [Sina Schorndorfer](sina.schorndorfer@imsb.uni-stuttgart.de)

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@ -3,6 +3,22 @@
2. Add your `statistic.jl` & "include" it.
3. Export all functions
4. Create a new environment in a separate folder and add the package.
5. Does `using MyStatsPackage` work now? :tada: congratulations!
6. Go back to your package environment. Now add a dependency (e.g. ProgressMeter) and a `compat`-entry
7. Go back to your project environment, has the dependency been updated? Think: should you use `resolve` or `instantiate`?
5. Does `using MyStatsPackage` work now?
:::{.callout collapse=true}
## Yes!
:tada: congratulations!
:::
:::{.callout collapse=true}
## No!
Oh no, better check you activated the right environment - ask for help!
:::
6. Go back to your package environment. Now add a dependency (e.g. ProgressMeter.jl) and a `compat`-entry
7. Go back to your project environment, has the
dependency been updated?
:::{.callout collapse=true}
## Hint?
Should you use `resolve` or `instantiate`?
:::

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material/1_mon/firststeps/tasks.qmd
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@ -10,13 +10,13 @@ You can mark some code and execute it using `ctrl` + `enter` - you can also gene
## The exercise
1. Open a new script `statistic_functions.jl` in VSCode in a folder of your choice.
2. implement a function called `rse_sum`^[rse = research software engineering, we could use `sum` in a principled way, but it requires some knowledge you likely don't have right now]. This function should return `true` if provided with the following test: `res_sum(1:36) == 666`. You should further make use of a for-loop.
2. implement a function called `rse_sum`^[rse = research software engineering, we could use `sum` in a principled way, but it requires some knowledge you likely don't have right now]. This function should return `true` if provided with the following test: `rse_sum(1:36) == 666`. You should further make use of a for-loop.
3. implement a second function called `rse_mean`, which calculates the mean of the provided vector. Make sure to use the `rse_sum` function! Test it using `res_mean(-15:17) == 1`
3. implement a second function called `rse_mean`, which calculates the mean of the provided vector. Make sure to use the `rse_sum` function! Test it using `rse_mean(-15:17) == 1`
4. Next implement a standard deviation function `rse_std`: $\sqrt{\frac{\sum(x-mean(x))}{n-1}}$, this time you should use elementwise/broadcasting operators. Test it with `rse_std(1:3) == 1`
4. Next implement a standard deviation function `rse_std`: $\sqrt{\frac{\sum((x-mean(x))^2)}{n-1}}$, this time you should use elementwise/broadcasting operators. Test it with `rse_std(1:3) == 1.`
5. Finally, we will implement `rse_tstat`, returning the t-value with `length(x)-1` DF, that the provided Array actually has a mean of 0. Test it with `rse_tstat(2:3) == 5`. Add the keyword argument `σ` that allows the user to optionally provide a pre-calculated standard deviation.
5. Finally, we will implement `rse_tstat`, returning the t-value with `length(x)-1` DF, that the provided Array actually has a mean of 0. The formula is $\frac{mean(x)}{std(x) / (sqrt(length(x)))}$ Test it with `rse_tstat(2:3) == 5.`. Add the keyword argument `σ` that allows the user to optionally provide a pre-calculated standard deviation.
Well done! You now have all functions defined with which we will continue our journey.

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format:
revealjs:
output-file: rse_basics_slides_revealjs.html
scrollable: true
progress: true
history: false
html: default
---

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---
type: slide
slideOptions:
transition: slide
width: 1400
height: 900
margin: 0.1
---
<style>
.reveal strong {
font-weight: bold;
color: orange;
}
.reveal p {
text-align: left;
}
.reveal section h1 {
color: orange;
}
.reveal section h2 {
color: orange;
}
.reveal code {
font-family: 'Ubuntu Mono';
color: orange;
}
.reveal section img {
background:none;
border:none;
box-shadow:none;
}
</style>
# Learning Goals
- Name and explain common workflows to automate in RSE.
- Explain the differences between the various continuous methodologies.
- Explain why automation is crucial in RSE.
- Write and understand basic automation scripts for GitHub Actions.
- s.t. we understand what `PkgTemplates` generates for us.
Material is taken and modified from the [SSE lecture](https://github.com/Simulation-Software-Engineering/Lecture-Material).
---
# 1. Workflow Automation
---
## Why Automation?
- Automatize tasks
- Run tests frequently, give feedback early etc.
- Ensure reproducible test environments
- Cannot forget automatized tasks
- Less burden to developer (and their workstation)
- Avoid manual errors
- Process often integrated in development workflow
- Example: Support by Git hooks or Git forges
---
## Typical Automation Tasks in RSE
- Check code formatting and quality
- Compile and test code for different platforms
- Generate coverage reports and visualization
- Build documentation and deploy it
- Build, package, and upload releases
---
## Continuous Methodologies (1/2)
- **Continuous Integration** (CI)
- Continuously integrate changes into "main" branch
- Avoids "merge hell"
- Relies on testing and checking code continuously
- Should be automatized
---
## Continuous Methodologies (2/2)
- **Continuous Delivery** (CD)
- Software is in a state that allows new release at any time
- Software package is built
- Actual release triggered manually
- **Continuous Deployment** (CD)
- Software is in a state that allows new release at any time
- Software package is built
- Actual release triggered automatically (continuously)
---
## Automation Services/Software
- [GitHub Actions](https://github.com/features/actions)
- [GitLab CI/CD](https://docs.gitlab.com/ee/ci/)
- [Circle CI](https://circleci.com/)
- [Travis CI](https://www.travis-ci.com/)
- [Jenkins](https://www.jenkins.io/)
- ...
---
# 2. GitHub Actions
---
## What is "GitHub Actions"?
> Automate, customize, and execute your software development workflows right in your repository with GitHub Actions.
From: [https://docs.github.com/en/actions](https://docs.github.com/en/actions)
---
## General Information
- Usage of GitHub's runners is [limited](https://docs.github.com/en/actions/learn-github-actions/usage-limits-billing-and-administration#usage-limits)
- Available for public repositories or accounts with subscription
- By default Actions run on GitHub's runners
- Linux, Windows, or MacOS
- Quickly evolving and significant improvements in recent years
---
## Components (1/2)
- [Workflow](https://docs.github.com/en/actions/using-workflows): Runs one or more jobs
- [Event](https://docs.github.com/en/actions/using-workflows/events-that-trigger-workflows): Triggers a workflow
- [Jobs](https://docs.github.com/en/actions/using-jobs): Set of steps (running on same runner)
- Steps executed consecutively and share data
- Jobs by default executed in parallel
- [Action](https://docs.github.com/en/actions/creating-actions): Application performing common, complex task (step) often used in workflows
- [Runner](https://docs.github.com/en/actions/learn-github-actions/understanding-github-actions#runners): Server that runs jobs
- [Artifacts](https://docs.github.com/en/actions/learn-github-actions/essential-features-of-github-actions#sharing-data-between-jobs): Files to be shared between jobs or to be kept after workflow finishes
---
## Components (2/2)
<img src="https://docs.github.com/assets/cb-25535/mw-1440/images/help/actions/overview-actions-simple.webp" width=95%; style="margin-left:auto; margin-right:auto; padding-top: 25px; padding-bottom: 25px; background: #eeeeee">
From [GitHub Actions tutorial](https://docs.github.com/en/actions)
---
## Setting up a Workflow
- Workflow file files stored `${REPO_ROOT}/.github/workflows`
- Configured via YAML file
```yaml
name: learn-github-actions
on: [push]
jobs:
check-bats-version:
runs-on: ubuntu-latest
steps:
- uses: actions/checkout@v2
- uses: actions/setup-node@v2
with:
node-version: '14'
- run: npm install -g bats
- run: bats -v
```
---
## Actions
```yaml
- uses: actions/checkout@v3
- uses: actions/setup-node@v2
with:
node-version: '14'
```
- Integrated via `uses` directive
- Additional configuration via `with` (options depend on Action)
- Find actions in [marketplace](https://github.com/marketplace?type=actions)
- Write [own actions](https://docs.github.com/en/actions/creating-actions)
---
## Some Useful Julia Actions
- Find on [gitHub.com/julia-actions](https://github.com/julia-actions/)
```
- uses: julia-actions/setup-julia@v1
with:
version: '1.9'
```
- More:
- `cache`: caches `~/.julia/artifacts/*` and `~/.julia/packages/*` to reduce runtime of CI
- `julia-buildpkg`: build package
- `julia-runtest`: run tests
- `julia-format`: format code
---
## User-specified Commands
```yaml
- name: "Single line command"
run: echo "Single line command"
- name: "Multi line command"
run: |
echo "First line"
echo "Second line. Directory ${PWD}"
workdir: tmp/
shell: bash
```
---
## Events
- Single or multiple events
```yaml
on: [push, fork]
```
- Activities
```yaml
on:
issue:
types:
- opened
- labeled
```
- Filters
```yaml
on:
push:
branches:
- main
- 'releases/**'
```
---
## Artifacts
- Data sharing between jobs and data upload
- Uploading artifact
```yaml
- name: "Upload artifact"
uses: actions/upload-artifact@v2
with:
name: my-artifact
path: my_file.txt
retention-days: 5
```
- Downloading artifact
```yaml
- name: "Download a single artifact"
uses: actions/download-artifact@v2
with:
name: my-artifact
```
**Note**: Drop name to download all artifacts
---
## Test Actions Locally
- [act](https://github.com/nektos/act)
- Relies extensively on Docker
- User should be in `docker` group
- Run `act` from root of the repository
```text
act (runs all workflows)
act --job WORKFLOWNAME
```
- Environment is not 100% identical to GitHub's
- Workflows may fail locally, but work on GitHub
---
## Further Reading
- [What is Continuous Integration?](https://www.atlassian.com/continuous-delivery/continuous-integration)
- [GitHub Actions documentation](https://docs.github.com/en/actions)
- [GitHub Actions quickstart](https://docs.github.com/en/actions/quickstart)
---
# 3. Demo: Automation with GitHub Actions
---
## Setting up a Test Job
- Import [Julia test package repository](https://github.com/uekerman/JuliaTestPackage) (the same code we used for testing)
- Set up workflow file
```bash
mkdir -p .github/workflows
cd .github/workflows
vi format-check.yml
```
- Let's check whether our code is formatted correctly. Edit `format-check.yml` to have following content
```yaml
name: format-check
on: [push, pull_request]
jobs:
format:
runs-on: ubuntu-latest
steps:
- uses: actions/checkout@v3
- uses: julia-actions/setup-julia@v1
with:
version: '1.9'
- name: Install JuliaFormatter and format
run: |
julia -e 'using Pkg; Pkg.add(PackageSpec(name="JuliaFormatter"))'
julia -e 'using JuliaFormatter; format(".", verbose=true)'
- name: Format check
run: |
julia -e '
out = Cmd(`git diff --name-only`) |> read |> String
if out == ""
exit(0)
else
@error "Some files have not been formatted"
write(stdout, out)
exit(1)
end'
```
- `runs-on` does **not** refer to a Docker container, but to a runner tag.
- Add, commit, push
- After the push, inspect "Action" panel on GitHub repository
- GitHub will schedule a run (yellow dot)
- Hooray. We have set up our first action.
- Failing test example:
- Edit settings on GitHub that one can only merge if all tests pass:
- Settings -> Branches -> Branch protection rule
- Choose `main` branch
- Enable "Require status checks to pass before merging". Optionally enable "Require branches to be up to date before merging"
- Choose status checks that need to pass: `test`
- Click on "Create" at bottom of page.
- Create a new branch `break-code`.
- Edit some file, violate the formatting, commit it and push it to the branch. Afterwards open a new PR and inspect the failing test. We are also not able to merge the changes as the "Merge" button should be inactive.
---
## act Demo
- `act` is for quick checks while developing workflows, not for developing the code
- Check available jobs (at root of repository)
```bash
act -l
```
- Run jobs for `push` event (default event)
```bash
act
```
- Run a specific job
```bash
act -j test
```
---
# 4. Exercise
Set up GitHub Actions for your statistics package. They should format your code and run the tests. To structure and parallelize things, you could use two separate jobs.

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@ -32,7 +32,7 @@ slideOptions:
}
</style>
## Learning Goals of the Git Lecture
# Learning Goals
- Refresh and organize students' existing knowledge on Git (learn how to learn more).
- Students can explain difference between merge and rebase and when to use what.
@ -232,7 +232,6 @@ Which level do you have?
- [Official documentation](http://git-scm.com/doc)
- [Video: Git in 15 minutes: basics, branching, no remote](https://www.youtube.com/watch?v=USjZcfj8yxE)
- [The GitHub Blog: Commits are snapshots, not diffs](https://github.blog/2020-12-17-commits-are-snapshots-not-diffs/)
- Chapters [6](https://merely-useful.tech/py-rse/git-cmdline.html) and [7](https://merely-useful.tech/py-rse/git-advanced.html) of Research Software Engineering with Python
- [Podcast All Things Git: History of VC](https://www.allthingsgit.com/episodes/the_history_of_vc_with_eric_sink.html)
- [git purr](https://girliemac.com/blog/2017/12/26/git-purr/)

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@ -3,6 +3,7 @@
1. Work with any forge that you like and create a user account (we strongly recommend GitHub since we will need it later again).
2. Push your package `MyStatsPackage` to a remote repository.
3. Add a function `printOwner` to the package through a pull request. The function should print your (GitHub) user name (hard-coded).
4. Use the package from somebody else in the classroom and verify with `printOwner` that you use the correct package.
5. Fork this other package and contribute a function `printContributor` to it via a PR. Get a review and get it merged.
6. Add more functions to other packages of classmates that print funny things, but always ensure a linear history.
4. Start a new Julia environment and use your package through its url: `]add https://github.com/[username]/MyStatsPackage`.
5. Now use the package from somebody else in the classroom instead and verify with `printOwner` that you use the correct package.
6. Fork this other package and contribute a function `printContributor` to it via a PR. Get a review and get it merged.
7. Add more functions to other packages of classmates that print funny things, but always ensure a linear history.

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@ -1,16 +1,44 @@
---
format: revealjs
type: slide
slideOptions:
transition: slide
width: 1400
height: 900
margin: 0.1
---
<style>
.reveal strong {
font-weight: bold;
color: orange;
}
.reveal p {
text-align: left;
}
.reveal section h1 {
color: orange;
}
.reveal section h2 {
color: orange;
}
.reveal code {
font-family: 'Ubuntu Mono';
color: orange;
}
.reveal section img {
background:none;
border:none;
box-shadow:none;
}
</style>
# Learning Goals
- Justify the effort of developing tests to some extent
- Get to know a few common terms of testing
- Work with the Julia unit testing package `Test.jl`
Material is taken and modified, on the one hand, from the [SSE lecture](https://github.com/Simulation-Software-Engineering/Lecture-Material), which builds partly on the [py-rse book](https://merely-useful.tech/py-rse), and, on the other hand, from the [Test.jl docs](https://docs.julialang.org/en/v1/stdlib/Test/).
Material is taken and modified from the [SSE lecture](https://github.com/Simulation-Software-Engineering/Lecture-Material), which builds partly on the [py-rse book](https://merely-useful.tech/py-rse), and from the [Test.jl docs](https://docs.julialang.org/en/v1/stdlib/Test/).
---
@ -20,30 +48,21 @@ Material is taken and modified, on the one hand, from the [SSE lecture](https://
## What is Testing?
- Smelling old milk before using it!
- A way to determine if a software is not producing reliable results and if so, what is the reason.
- Manual testing vs. automated testing.
- Smelling old milk before using it
- A way to determine if a software is not producing reliable results and if so, what is the reason
- Manual testing vs. automated testing
---
## Why Should you Test your Software?
- Improve software reliability and reproducibility.
- Make sure that changes (bugfixes, new features) do not affect other parts of software.
- Improve software reliability and reproducibility
- Make sure that changes (bugfixes, new features) do not affect other parts of software
- Generally all software is better off being tested regularly. Possible exceptions are very small codes with single users.
- Ensure that a released version of a software actually works.
---
## Nomenclature in Software Testing
- **Fixture**: preparatory set for testing.
- **Actual result**: what the code produces when given the fixture.
- **Expected result**: what the actual result is compared to.
- **Test coverage**: how much of the code do tests touch in one run.
---
## Some Ways to Test Software
- Assertions
@ -55,29 +74,27 @@ Material is taken and modified, on the one hand, from the [SSE lecture](https://
## Assertions
- Principle of *defensive programming*.
```julia
@assert condition "message"
```
- Principle of *defensive programming*
- Nothing happens when an assertion is true; throws error when false.
- Types of assertion statements:
- Precondition
- Postcondition
- Invariant
- A basic but powerful tool to test a software on-the-go.
- Assertion statement syntax in Python
```julia
@assert condition "message"
```
- A basic but powerful tool to test a software on-the-go
---
## Unit Testing
- Catching errors with assertions is good but preventing them is better!
- Catching errors with assertions is good but preventing them is better.
- A *unit* is a single function in one situation.
- A situation is one amongst many possible variations of input parameters.
- User creates the expected result manually.
- Fixture is the set of inputs used to generate an actual result.
- Actual result is compared to the expected result by `@test`.
- User creates the **expected result** manually.
- **Actual result** is compared to the expected result by `@test`.
---
@ -85,109 +102,44 @@ Material is taken and modified, on the one hand, from the [SSE lecture](https://
- Test whether several units work in conjunction.
- *Integrate* units and test them together in an *integration* test.
- Often more complicated than a unit test and has more test coverage.
- A fixture is used to generate an actual result.
- Actual result is compared to the expected result by `@test`.
- Often more complicated than a unit test and gives higher test coverage.
---
## Regression Testing
- Generating an expected result is not possible in some situations.
- Compare the current actual result with a previous actual result.
- Compare the *current* actual result with a *previous* actual result.
- No guarantee that the current actual result is correct.
- Risk of a bug being carried over indefinitely.
- Main purpose is to identify changes in the current state of the code with respect to a past state.
---
## Test Coverage
- Coverage is the amount of code a test touches in one run.
- Aim for high test coverage.
- There is a trade-off: high test coverage vs. effort in test development
---
## Comparing Floating-point Variables
- Very often quantities in math software are `float` / `double`.
- Such quantities cannot be compared to exact values, an approximation is necessary.
- Comparison of floating point variables needs to be done to a certain tolerance.
```julia
@test 1 ≈ 0.999999 rtol=1e-5
```
- Get `≈` by Latex `\approx` + TAB
---
## Test-driven Development (TDD)
- Principle is to write a test and then write a code to fulfill the test.
- Advantages:
- In the end user ends up with a test alongside the code.
- Eliminates confirmation bias of the user.
- Writing tests gives clarity on what the code is supposed to do.
- Disadvantage: known to not improve productivity.
---
## Checking-driven Development (CDD)
- Developer performs spot checks; sanity checks at intermediate stages
- Math software often has heuristics which are easy to determine.
- Keep performing same checks at different stages of development to ensure the code works.
---
## Verifying a Test
- Test written as part of a bug-fix:
- Reproduce the bug in the test by ensuring that the test fails.
- Fix the bug.
- Rerun the test to ensure that it passes.
- Test written to increase code coverage:
- Make sure that the first iteration of the test passes.
- Try introducing a small fixable bug in the code to verify if the test fails.
---
# 2. Unit Testing in Julia with Test.jl
---
## Setup of Tests.jl
## Setup of Test.jl
- Standard library to write and manage tests, `using Test`
- Standardized folder structure:
```
├── Manifest.toml
├── Project.toml
├── src/
└── test
├── Manifest.toml
├── Project.toml
├── runtests.jl
└── setup.jl
```
```
├── Manifest.toml
├── Project.toml
├── src/
└── test
├── Manifest.toml
├── Project.toml
├── runtests.jl
└── setup.jl
```
- Singular `test` vs plural `runtests.jl`
- `setup.jl` for all `using XYZ` statements, included in `runtests.jl`
- Additional packages either in `[extra] section` of `./Project.toml` or in a new `./test/Project.toml` environment
- Additional packages in `[extra] section` of `./Project.toml` or in new `./test/Project.toml`
- In case of the latter: Do not add the package itself to the `./test/Project.toml`
---
## Run Tests
Various options:
- Directly call `runtests.jl` TODO?
- From Pkg-Manager `]test` when root project is activated
- Run: `]test` when root project is activated
---
@ -206,11 +158,11 @@ Various options:
- `@testset`: Structure tests
```julia
julia> @testset "trigonometric identities" begin
θ = 2/3*π
@test sin(-θ) ≈ -sin(θ)
@test cos(-θ) ≈ cos(θ)
end;
@testset "trigonometric identities" begin
θ = 2/3*π
@test sin(-θ) ≈ -sin(θ)
@test cos(-θ) ≈ cos(θ)
end;
```
- `@testset for ... end`: Test in loop
@ -223,6 +175,8 @@ Various options:
- [HiRSE-Summer of Testing Part 2b: "Testing with Julia" by Nils Niggemann](https://www.youtube.com/watch?v=gSMKNbZOpZU)
- [Official documentation of Test.jl](https://docs.julialang.org/en/v1/stdlib/Test/)
---
# 3. Test.jl Demo
We use [`MyTestPackage`](https://github.com/s-ccs/summerschool_simtech_2023/tree/main/material/2_tue/testing/MyTestPackage), which looks as follows:
@ -246,7 +200,7 @@ We use [`MyTestPackage`](https://github.com/s-ccs/summerschool_simtech_2023/tree
- Look at `MyTestPackage.jl` and `find.jl`: We have two functions `find_max` and `find_mean`, which calculate the maximum and mean of all elements of a `::AbstractVector`.
- Assertions were added to check for `NaN` values
- Look at `runtests.jl`:
- TODO: Why do we need `using MyTestPackage`?
- Why do we need `using MyTestPackage`?
- We include dependencies via `setup.jl`: `Test` and `StableRNG`.
- Testset "find"
- Look at `find.jl`

48
material/3_wed/regression/Code_Snippets.jl Normal file
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@ -0,0 +1,48 @@
using Statistics
using Plots
using RDatasets
using GLM
#---
trees = dataset("datasets", "trees")
scatter(trees.Girth, trees.Volume,
legend=false, xlabel="Girth", ylabel="Volume")
#---
scatter(trees.Girth, trees.Volume,
legend=false, xlabel="Girth", ylabel="Volume")
plot!(x -> -37 + 5*x)
#---
linmod1 = lm(@formula(Volume ~ Girth), trees)
#---
linmod2 = lm(@formula(Volume ~ Girth + Height), trees)
#---
r2(linmod1)
r2(linmod2)
linmod3 = lm(@formula(Volume ~ Girth + Height + Girth*Height), trees)
r2(linmod3)
#---
using CSV
using HTTP
http_response = HTTP.get("https://vincentarelbundock.github.io/Rdatasets/csv/AER/SwissLabor.csv")
SwissLabor = DataFrame(CSV.File(http_response.body))
SwissLabor[!,"participation"] .= (SwissLabor.participation .== "yes")
#---
model = glm(@formula(participation ~ age), SwissLabor, Binomial(), ProbitLink())

113
material/3_wed/regression/MultipleRegressionBasics.qmd
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@ -10,13 +10,26 @@ editor:
### Introductory Example: tree dataset from R
\[figure of raw data\]
``` julia
using Statistics
using Plots
using RDatasets
trees = dataset("datasets", "trees")
scatter(trees.Volume, trees.Girth,
legend=false, xlabel="Girth", ylabel="Volume")
```
*Aim:* Find relationship between the *response variable* `volume` and
the *explanatory variable/covariate* `girth`? Can we predict the volume
of a tree given its girth?
\[figure including a straight line\]
``` julia
scatter(trees.Girth, trees.Volume,
legend=false, xlabel="Girth", ylabel="Volume")
plot!(x -> -37 + 5*x)
```
First Guess: There is a linear relation!
@ -52,8 +65,10 @@ Note: There is a closed-form expression for
$(\hat \beta_0, \hat \beta_1)$. We will not make use of it here, but
rather use Julia to solve the problem.
\[use Julia code (existing package) to perform linear regression for
`volume ~ girth`\]
``` julia
lm(@formula(Volume ~ Girth), trees)
```
*Interpretation of the Julia output:*
@ -70,9 +85,13 @@ rather use Julia to solve the problem.
Under the hypothesis $\beta_i=0$, the test statistics $t_i$ would
follow a $t$-distribution.
- column `Pr(>|t|)`: $p$-values for the hyptheses $\beta_i=0$ for
- column `Pr(>|t|)`: $p$-values for the hypotheses $\beta_i=0$ for
$i=0,1$
:::callout.tip
The command `rand(n)` generates a sample of `n` "random" (i.e., uniformly distributed) random numbers.
:::
**Task 1**: Generate a random set of covariates $\mathbf{x}$. Given
these covariates and true parameters $\beta_0$, $\beta_1$ and $\sigma^2$
(you can choose them)), simulate responses from a linear model and
@ -166,6 +185,15 @@ the corresponding standard errors and the $t$-statistics. Test your
functions with the \`\`\`tree''' data set and try to reproduce the
output above.
``` julia
r2(linmod1)
r2(linmod2)
linmod3 = lm(@formula(Volume ~ Girth + Height + Girth*Height), trees)
r2(linmod3)
```
## Generalized Linear Models
Classical linear model
@ -206,29 +234,35 @@ $$
For the models above, these are:
+----------------------+---------------------+----------------------+
| Type of Data | Distribution Family | Link Function |
+======================+=====================+======================+
| continuous | Normal | identity: |
| | | |
| | | $$ |
| | | g(x)=x |
| | | $$ |
+----------------------+---------------------+----------------------+
| count | Poisson | log: |
| | | |
| | | $$ |
| | | g(x) = \log(x) |
| | | $$ |
+----------------------+---------------------+----------------------+
| binary | Bernoulli | logit: |
| | | |
| | | $$ |
| | | g(x) = \log\left |
| | | ( |
| | | \frac{x}{1-x}\right) |
| | | $$ |
+----------------------+---------------------+----------------------+
+----------------+------------------+-----------------+
| Type of Data | Distribution | Link Function |
| | Family | |
+================+==================+=================+
| continuous | Normal | identity: |
| | | |
| | | $$ |
| | | g(x)=x |
| | | $$ |
+----------------+------------------+-----------------+
| count | Poisson | log: |
| | | |
| | | $$ |
| | | g(x) = \log(x) |
| | | $$ |
+----------------+------------------+-----------------+
| binary | Bernoulli | logit: |
| | | |
| | | $$ |
| | | g |
| | | (x) = \log\left |
| | | ( |
| | | \ |
| | | f |
| | | ra |
| | | c |
| | | {x}{1-x}\right) |
| | | $$ |
+----------------+------------------+-----------------+
In general, the parameter vector $\beta$ is estimated via maximizing the
likelihood, i.e.,
@ -246,8 +280,23 @@ $$
In the Gaussian case, the maximum likelihood estimator is identical to
the least squares estimator considered above.
\[\[ Example in Julia: maybe `SwissLabor` \]\]
``` julia
using CSV
using HTTP
**Task 3:** Reproduce the results of our data analysis of the `tree`
data set using a generalized linear model with normal distribution
family.
http_response = HTTP.get("https://vincentarelbundock.github.io/Rdatasets/csv/AER/SwissLabor.csv")
SwissLabor = DataFrame(CSV.File(http_response.body))
SwissLabor[!,"participation"] .= (SwissLabor.participation .== "yes")
model = glm(@formula(participation ~ age^2),
SwissLabor, Binomial(), ProbitLink())
```
::: callout-task
**Task 3**:
1. Reproduce the results of our data analysis of the `tree` data set using
a generalized linear model with normal distribution family.
2. Generate
:::