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‎.flake8

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#########################
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# Flake8 Configuration #
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# (.flake8) #
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#########################
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[flake8]
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ignore =
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# asserts are ok when testing.
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S101
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# pickle
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S301
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# pickle
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S403
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S404
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S603
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# Line break before binary operator (flake8 is wrong)
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W503
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# Ignore the spaces black puts before columns.
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E203
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# allow path extensions for testing.
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E402
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DAR101
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DAR201
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# flake and pylance disagree on linebreaks in strings.
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N400
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exclude =
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.tox,
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.git,
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__pycache__,
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docs/source/conf.py,
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build,
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dist,
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tests/fixtures/*,
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*.pyc,
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*.bib,
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*.egg-info,
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.cache,
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.eggs,
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data.
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max-line-length = 120
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max-complexity = 20
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import-order-style = pycharm
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application-import-names =
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seleqt
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tests

‎.github/workflows/test.yml

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name: Tests
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on: [ push, pull_request ]
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jobs:
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tests:
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name: Tests
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runs-on: ${{ matrix.os }}
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strategy:
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matrix:
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os: [ ubuntu-latest ]
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python-version: [3.11.0]
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steps:
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- uses: actions/checkout@v2
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- name: Set up Python ${{ matrix.python-version }}
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uses: actions/setup-python@v2
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with:
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python-version: ${{ matrix.python-version }}
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- name: Install dependencies
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run: pip install nox
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- name: Test with pytest
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run:
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nox -s test
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lint:
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name: Lint
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runs-on: ubuntu-latest
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strategy:
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matrix:
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python-version: [3.11.0]
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steps:
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- uses: actions/checkout@v2
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- name: Set up Python ${{ matrix.python-version }}
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uses: actions/setup-python@v2
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with:
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python-version: ${{ matrix.python-version }}
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- name: Install dependencies
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run: pip install nox
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- name: Run flake8
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run: nox -s lint
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- name: Run mypy
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run: nox -s typing

‎.gitignore

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.vscode/
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# Byte-compiled / optimized / DLL files
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__pycache__/
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*.py[cod]
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*$py.class
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# C extensions
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*.so
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# Distribution / packaging
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.Python
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build/
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develop-eggs/
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dist/
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downloads/
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eggs/
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.eggs/
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lib/
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lib64/
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parts/
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sdist/
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var/
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wheels/
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share/python-wheels/
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*.egg-info/
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.installed.cfg
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*.egg
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MANIFEST
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# PyInstaller
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# Usually these files are written by a python script from a template
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# before PyInstaller builds the exe, so as to inject date/other infos into it.
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*.manifest
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*.spec
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# Installer logs
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pip-log.txt
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pip-delete-this-directory.txt
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# Unit test / coverage reports
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htmlcov/
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.tox/
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.nox/
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.coverage
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.coverage.*
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.cache
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nosetests.xml
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coverage.xml
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*.cover
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*.py,cover
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.hypothesis/
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.pytest_cache/
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cover/
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# Translations
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*.mo
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*.pot
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# Django stuff:
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*.log
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local_settings.py
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db.sqlite3
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db.sqlite3-journal
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# Flask stuff:
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instance/
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.webassets-cache
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# Scrapy stuff:
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.scrapy
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# Sphinx documentation
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docs/_build/
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# PyBuilder
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.pybuilder/
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target/
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# Jupyter Notebook
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.ipynb_checkpoints
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# IPython
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profile_default/
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ipython_config.py
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# pyenv
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# For a library or package, you might want to ignore these files since the code is
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# intended to run in multiple environments; otherwise, check them in:
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# .python-version
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# pipenv
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# According to pypa/pipenv#598, it is recommended to include Pipfile.lock in version control.
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# However, in case of collaboration, if having platform-specific dependencies or dependencies
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# having no cross-platform support, pipenv may install dependencies that don't work, or not
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# install all needed dependencies.
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#Pipfile.lock
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# poetry
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# Similar to Pipfile.lock, it is generally recommended to include poetry.lock in version control.
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# This is especially recommended for binary packages to ensure reproducibility, and is more
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# commonly ignored for libraries.
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# https://python-poetry.org/docs/basic-usage/#commit-your-poetrylock-file-to-version-control
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#poetry.lock
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# pdm
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# Similar to Pipfile.lock, it is generally recommended to include pdm.lock in version control.
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#pdm.lock
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# pdm stores project-wide configurations in .pdm.toml, but it is recommended to not include it
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# in version control.
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# https://pdm.fming.dev/#use-with-ide
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.pdm.toml
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# PEP 582; used by e.g. github.com/David-OConnor/pyflow and github.com/pdm-project/pdm
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__pypackages__/
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# Celery stuff
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celerybeat-schedule
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celerybeat.pid
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# SageMath parsed files
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*.sage.py
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# Environments
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.env
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.venv
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env/
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venv/
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ENV/
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env.bak/
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venv.bak/
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# Spyder project settings
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.spyderproject
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.spyproject
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# Rope project settings
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.ropeproject
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# mkdocs documentation
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/site
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# mypy
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.mypy_cache/
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.dmypy.json
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dmypy.json
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# Pyre type checker
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.pyre/
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# pytype static type analyzer
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.pytype/
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# Cython debug symbols
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cython_debug/
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# PyCharm
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# JetBrains specific template is maintained in a separate JetBrains.gitignore that can
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# be found at https://github.com/github/gitignore/blob/main/Global/JetBrains.gitignore
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# and can be added to the global gitignore or merged into this file. For a more nuclear
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# option (not recommended) you can uncomment the following to ignore the entire idea folder.
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#.idea/

‎README.md

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# Optimization Exercise
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During this exercise, you will implement gradient descent to solve optimization problems.
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For all activities, the task is to find the lowest point on a function surface or in
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mathematical language
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$$ \min_{x}f(x) .$$
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All modules in `src` require your attention.
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- To get started, take a look at `src/optimize_1d.py`.
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Use the gradient to find the minumum of the parabola starting from five, or in other words
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$$ \min_{x} x^2, \text{ with } x_0 = 5 .$$
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The problem is illustrated below:
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![parabola_task](./figures/parabola_task.png)
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- Next we consider a paraboloid, $\cdot$ denotes the scalar product,
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$$ \min_{\mathbf{x}} \mathbf{x} \cdot \mathbf{x}, \text{ with } \mathbf{x_0} = (2.9, -2.9) .$$
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The paraboloid is already implemented in `src/optimize_2d.py`.
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Your task is to solve this problem using two-dimensional gradient descent.
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Once more the problem is illustrated below:
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![paraboloid_task](./figures/paraboloid_task.png)
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- Additionally we consider a bumpy paraboloid, $\cdot$ denotes the scalar product,
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$$ \min_{\mathbf{x}} \mathbf{x} \cdot \mathbf{x} + \cos(2 \pi x_0) + \sin(2 \pi x_1 ), \text{ with } \mathbf{x_0} = (2.9, -2.9) .$$
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The addtional sin and cosine terms will require momentum for convergence.
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The bumpy paraboloid is already implemented in `src/optimize_2d_momentum_bumpy.py`.
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Your task is to solve this problem using two-dimensional gradient descent with momentum.
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Once more the problem is illustrated below:
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![bumpy_paraboloid_task](./figures/bumpy_paraboloid_task.png)
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- Finally, to explore the automatic differentiation functionality we consider the problem,
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$$ \min_{\mathbf{x}} \mathbf{x} \cdot \mathbf{x} + \cos(2 \pi x_0 ) + \sin(2 \pi x_1) + 0.5 \cdot \text{relu}(x_0) + 10 \cdot \tanh( \|\mathbf{x} \| ), \text{ with } \mathbf{x_0} = (2.9, -2.9) .$$
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The function is already defined in `src/optimize_2d_momentum_bumpy_torch.py`. We dont have to find the gradient by hand!
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Use `torch.func.grad` [(torch-documentation)](https://pytorch.org/docs/stable/generated/torch.func.grad.html) to compute the gradient automatically. Use the result to find the minimum using momentum.
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While coding use `nox -s test`, `nox -s lint`, and `nox -s typing` to check your code.
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Autoformatting help is available via `nox -s format`.
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Feel free to read mode about nox at https://nox.thea.codes/en/stable/ .

‎figures/bumpy_paraboloid_task.png

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‎figures/parabola_task.png

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‎figures/paraboloid_task.png

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‎noxfile.py

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"""This module implements our CI function calls."""
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import nox
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@nox.session(name="test")
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def run_test(session):
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"""Run pytest."""
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session.install("-r", "requirements.txt")
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session.install("pytest")
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session.run("pytest")
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@nox.session(name="lint")
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def lint(session):
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"""Check code conventions."""
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session.install("flake8==4.0.1")
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session.install(
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"flake8-black",
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"flake8-docstrings",
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"flake8-bugbear",
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"flake8-broken-line",
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"pep8-naming",
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"pydocstyle",
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"darglint",
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)
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session.run("flake8", "src", "tests", "noxfile.py")
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@nox.session(name="typing")
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def mypy(session):
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"""Check type hints."""
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session.install("-r", "requirements.txt")
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session.install("mypy")
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session.run(
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"mypy",
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"--install-types",
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"--non-interactive",
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"--ignore-missing-imports",
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"--no-strict-optional",
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"--no-warn-return-any",
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"--implicit-reexport",
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"--allow-untyped-calls",
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"src",
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)
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@nox.session(name="format")
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def format(session):
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"""Fix common convention problems automatically."""
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session.install("black")
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session.install("isort")
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session.run("isort", "src", "tests", "noxfile.py")
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session.run("black", "src", "tests", "noxfile.py")

‎pytest.ini

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[pytest]
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markers =
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slow: this test is slow and should only run locally.
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pythonpath = .

‎requirements.txt

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nox
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numpy
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matplotlib
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torch

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