Initial commit

.gitignore

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

README.md

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+# Репозиторий для работ по вычислительной математике

lab1/main.py

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+import numpy as np
+
+
+def point_info(x, f):
+    return f'x = {x}, f(x) = {f(x)}'
+
+
+def hooke_jeeves(f, x0, delta0, epsilon, alpha):
+    x = np.array(x0)
+    delta = np.array(delta0)
+
+    iteration = 0
+
+    while np.linalg.norm(delta) > epsilon:
+        iteration += 1
+
+        print()
+        print('=' * 40)
+        print('Итерация', iteration)
+
+        print('Текущая базовая точка', point_info(x, f))
+
+        sample_x = exploratory_search(f, x, delta)
+
+        if f(sample_x) < f(x):
+            print('Исследующий поиск УДАЧНЫЙ')
+
+            x_p = sample_search(f, x, sample_x)
+
+            if f(x_p) < f(x):
+                print('Поиск по образцу УДАЧНЫЙ')
+                x = x_p
+            else:
+                print('Поиск по образцу ПРОВАЛЕН')
+                x = sample_x
+
+            print()
+            print('Новая базовая точка', point_info(x, f))
+
+        else:
+            print('Исследующий поиск ПРОВАЛЕН')
+
+            print('Уменьшаем шаг', delta, '->', delta / alpha)
+            delta = delta / alpha
+            print('ε =', np.linalg.norm(delta))
+
+    return x, f(x)
+
+
+def exploratory_search(f, x, delta):
+    print()
+    print('Выполняем исследующий поиск')
+
+    x_new = np.array(x)
+    f_x_new = f(x_new)
+
+    for i in range(len(x)):
+        x_up = x_new.copy()
+        x_down = x_new.copy()
+
+        x_up[i] += delta[i]
+        x_down[i] -= delta[i]
+
+        f_x_up = f(x_up)
+        f_x_down = f(x_down)
+
+        if (f_x_up < f_x_new and f_x_up < f_x_down):
+            x_new = x_up
+            f_x_new = f_x_up
+        elif (f_x_down < f_x_new):
+            x_new = x_down
+            f_x_new = f_x_down
+
+    if (any([x_new[i] != x[i] for i in range(len(x))])):
+        print('Найдена точка', x_new, f(x_new))
+    return x_new
+
+
+def sample_search(f, x1, x2):
+    print()
+    print('Выполняем поиск по образцу')
+    while f(x2) < f(x1):
+        x2, x1 = x2 + (x2 - x1), x2
+    print('Найдена точка', x2, f(x2))
+    return x2
+
+
+def f1():
+    x0 = [1, 0, 0]
+    delta0 = [1e+6, 1e+6, 1e+6]
+    alpha = 2
+    epsilon = 1e-4
+    def f(x): return x[0] ** 2 + 2 * x[1] ** 2 + 5 * \
+        x[2] ** 2 - 2 * x[0] * x[1] - 4 * x[0] * x[2] - 2 * x[2]
+
+
+def f2():
+    x0 = [1, 1]
+    delta0 = [1, 1]
+    alpha = 2
+    epsilon = 1e-6
+
+    def f(x): return x[0] ** 4 + x[1] ** 2 - 4 * x[0] * x[1]
+
+    x, val = hooke_jeeves(f, x0, delta0, epsilon, alpha)
+    return x, val
+
+
+def f3():
+    x0 = [1, 0]
+    delta0 = [1, 1]
+    alpha = 2
+    epsilon = 1e-5
+
+    def f(x): return x[0] * np.exp(x[0]) - (1 + np.exp(x[0])) * np.sin(x[1])
+
+    x, val = hooke_jeeves(f, x0, delta0, epsilon, alpha)
+    return x, val
+
+
+def example():
+    x0 = [-4, -4]
+    delta0 = [1, 1]
+    alpha = 2
+    epsilon = 1e-4
+
+    def f(x): return 8 * (x[0] ** 2) + 4 * x[0] * x[1] + 5 * (x[1] ** 2)
+
+    x, val = hooke_jeeves(f, x0, delta0, epsilon, alpha)
+    return x, val
+
+
+# x, val = f1()
+# x, val = f2()
+# x, val = f3()
+x, val = example()
+
+print()
+print('=' * 40)
+print("Точка экстремумв:", x)
+print("Минимальное значение функции:", val)

lab1/requirements.txt

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+numpy==2.2.3