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diff --git a/4 вычмат/лабораторные/lab2/.editorconfig b/4 вычмат/лабораторные/lab2/.editorconfig
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--- /dev/null
+++ b/4 вычмат/лабораторные/lab2/.editorconfig
@@ -0,0 +1,18 @@
+# This file is for unifying the coding style for different editors and IDEs
+# editorconfig.org
+
+root = true
+
+[*]
+charset = utf-8
+end_of_line = lf
+trim_trailing_whitespace = true
+insert_final_newline = true
+indent_style = space
+indent_size = 4
+
+[*.py]
+indent_size = 2
+
+[*.md]
+trim_trailing_whitespace = false
diff --git a/4 вычмат/лабораторные/lab2/.gitattributes b/4 вычмат/лабораторные/lab2/.gitattributes
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--- /dev/null
+++ b/4 вычмат/лабораторные/lab2/.gitattributes
@@ -0,0 +1,3 @@
+*.pyc linguist-generated=true
+*.pyo linguist-generated=true
+*.pyd linguist-generated=true
diff --git a/4 вычмат/лабораторные/lab2/.gitignore b/4 вычмат/лабораторные/lab2/.gitignore
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index 0000000..842cea6
--- /dev/null
+++ b/4 вычмат/лабораторные/lab2/.gitignore
@@ -0,0 +1,165 @@
+# Graphics
+*.png
+
+# 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
+
+# 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/#use-with-ide
+.pdm.toml
+
+# 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
+
+# Rope project settings
+.ropeproject
+
+# mkdocs documentation
+/site
+
+# mypy
+.mypy_cache/
+.dmypy.json
+dmypy.json
+
+# Pyre type checker
+.pyre/
+
+# pytype static type analyzer
+.pytype/
+
+# Cython debug symbols
+cython_debug/
+
+## IntelliJ IDEA
+.idea/
+.idea_modules/
+.iws
+
+## Misc
+*.DS_Store
diff --git a/4 вычмат/лабораторные/lab2/LICENSE b/4 вычмат/лабораторные/lab2/LICENSE
new file mode 100644
index 0000000..f288702
--- /dev/null
+++ b/4 вычмат/лабораторные/lab2/LICENSE
@@ -0,0 +1,674 @@
+ GNU GENERAL PUBLIC LICENSE
+ Version 3, 29 June 2007
+
+ Copyright (C) 2007 Free Software Foundation, Inc.
+ Everyone is permitted to copy and distribute verbatim copies
+ of this license document, but changing it is not allowed.
+
+ Preamble
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+
+ Nothing in this License shall be construed as excluding or limiting
+any implied license or other defenses to infringement that may
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+
+ 12. No Surrender of Others' Freedom.
+
+ If conditions are imposed on you (whether by court order, agreement or
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+ 13. Use with the GNU Affero General Public License.
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+Also add information on how to contact you by electronic and paper mail.
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+ If the program does terminal interaction, make it output a short
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+ You should also get your employer (if you work as a programmer) or school,
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+.
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+Public License instead of this License. But first, please read
+.
diff --git a/4 вычмат/лабораторные/lab2/README.md b/4 вычмат/лабораторные/lab2/README.md
new file mode 100644
index 0000000..30a4db7
--- /dev/null
+++ b/4 вычмат/лабораторные/lab2/README.md
@@ -0,0 +1,72 @@
+# Лабораторная работа 2
+
+## Вариант `2`
+
+
+
+> «Численное решение нелинейных уравнений и систем»
+
+|.pdf|.docx|
+|-|-|
+| [report](./docs/report.pdf) | [report](./docs/report.docx) |
+
+---
+
+## Задание ЛР №2
+
+[Задание ЛР №2](../../задания/Задание%20ЛР№2.pdf)
+
+Цель работы: изучить численные методы решения нелинейных уравнений и их
+систем, найти корни заданного нелинейного уравнения/системы нелинейных уравнений,
+выполнить программную реализацию методов.
+
+**Лабораторная работа состоит из двух частей: вычислительной и программной.**
+
+## Содержание отчета:
+
+- Титульный лист.
+- Цель лабораторной работы.
+- Порядок выполнения работы.
+- Рабочие формулы используемых методов.
+- Графики функций на исследуемом интервале.
+- Заполненные таблицы вычислительной части 1 лабораторной работы (в зависимости от варианта: табл. 1 – 5).
+- Решение системы нелинейных уравнений (вычислительная часть 2).
+- Листинг программы, по крайней мере, коды используемых методов.
+- Результаты выполнения программы при различных исходных данных.
+- Выводы
+
+## Контрольные вопросы к защите лабораторной работы:
+
+1. Понятие точного и приближенного решений нелинейного уравнения.
+2. Основная идея метода половинного деления?
+3. Может ли метод половинного деления найти точное значение корня уравнения?
+4. В чем суть метода Ньютона?
+5. Как выбирается начальное приближение для метода Ньютона?
+6. Идея метода хорд?
+7. Как выбирается начальное приближение для метода хорд с фиксированным концом
+интервала изоляции корня?
+8. По каким причинам методы хорд и касательных предпочтительнее метода простой
+итерации?
+9. Какой из методов является двухшаговым методом? Как запустить этот метод?
+10. В чем суть метода простой итерации?
+11. Каковы условия применяемости метода простой итерации?
+12. Как правильно преобразовать исходное нелинейное уравнение $y = f(x)$ к виду $x = \phi(x)$?
+13. Каковы основные критерии окончания итерационного процесса?
+14. Как оценить необходимое количество итераций в методе биссекции при заданной
+точности?
+15. Алгоритм решения системы нелинейных уравнений методом Ньютона?
+16. Каковы преимущества и недостатки графического метода отделения решения для
+системы двух нелинейных уравнений?
+17. В каких случаях можно применить метод простой итерации для решения системы
+нелинейных уравнений?
+18. Когда можно считать итерационный процесс законченным при использовании метода простой итерации для решения системы нелинейных уравнений?
+19. Что такое сходимость и скорость сходимости численных методов?
+20. Дайте определение устойчивости итерационного метода?
+
+## Лицензия
+
+Проект доступен с открытым исходным кодом на условиях [Лицензии GNU GPL 3](https://opensource.org/license/gpl-3-0/).
+
+*Авторские права 2023 Max Barsukov*
+
+**Поставьте звезду :star:, если вы нашли этот проект полезным.**
diff --git a/4 вычмат/лабораторные/lab2/docs/report.docx b/4 вычмат/лабораторные/lab2/docs/report.docx
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diff --git a/4 вычмат/лабораторные/lab2/docs/report.pdf b/4 вычмат/лабораторные/lab2/docs/report.pdf
new file mode 100644
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diff --git a/4 вычмат/лабораторные/lab2/src/dto/equation.py b/4 вычмат/лабораторные/lab2/src/dto/equation.py
new file mode 100644
index 0000000..bc88d71
--- /dev/null
+++ b/4 вычмат/лабораторные/lab2/src/dto/equation.py
@@ -0,0 +1,30 @@
+from typing import Callable
+import matplotlib.pyplot as plt
+import numpy as np
+from scipy.misc import derivative
+
+
+dx = 0.00001
+
+class Equation:
+ def __init__(self, function: Callable, text: str):
+ self.text = text
+ self.function = function
+
+ def draw(self, left: float, right: float):
+ x = np.linspace(left, right)
+ func = np.vectorize(self.function)(x)
+
+ plt.title = 'График заданной функции'
+ plt.grid(True, which='both')
+ plt.xlabel('X')
+ plt.ylabel('Y')
+ plt.axhline(y=0, color='gray', label='y = 0')
+ plt.plot(x, func, 'blue', label=self.text)
+ plt.legend(loc='upper left')
+ plt.savefig('graph.png')
+ plt.show()
+
+ def root_exists(self, left: float, right: float):
+ return (self.function(left) * self.function(right) < 0) \
+ and (derivative(self.function, left, dx) * derivative(self.function, left, dx) > 0)
diff --git a/4 вычмат/лабораторные/lab2/src/dto/result.py b/4 вычмат/лабораторные/lab2/src/dto/result.py
new file mode 100644
index 0000000..47306f9
--- /dev/null
+++ b/4 вычмат/лабораторные/lab2/src/dto/result.py
@@ -0,0 +1,15 @@
+from dataclasses import dataclass
+
+
+@dataclass
+class Result:
+ root: float
+ function_value_at_root: float
+ iterations: int
+ decimal_places: int
+
+ def __str__(self):
+ return 'Результат:\n' \
+ f'Найденный корень уравнения: {round(self.root, self.decimal_places)}\n' \
+ f'Значение функции в корне: {self.function_value_at_root}\n' \
+ f'Число итераций: {self.iterations}'
diff --git a/4 вычмат/лабораторные/lab2/src/main.py b/4 вычмат/лабораторные/lab2/src/main.py
new file mode 100644
index 0000000..f5d0c89
--- /dev/null
+++ b/4 вычмат/лабораторные/lab2/src/main.py
@@ -0,0 +1,77 @@
+import math
+
+from dto.equation import Equation
+from methods.half_division_method import HalfDivisionMethod
+from methods.newton_method import NewtonMethod
+from methods.simple_iterations_method import SimpleIterationsMethod
+from methods.chord_method import ChordMethod
+
+import system_of_equation
+import mainboilerplate
+
+methods = {
+ 1: HalfDivisionMethod,
+ 2: ChordMethod,
+ 3: SimpleIterationsMethod,
+ 4: NewtonMethod
+}
+
+predefined_functions = {
+ 1: Equation(lambda x: (-1.38*x**3 - 5.42*x**2 + 2.57*x + 10.95), '-1.38*x^3 - 5.42*x^2 + 2.57*x + 10.95'),
+ 2: Equation(lambda x: (x**3 - 1.89*x**2 - 2*x + 1.76), 'x^3 - 1.89*x^2 - 2*x + 1.76'),
+ # https://cutt.ly/6zNbCha
+ 3: Equation(lambda x: (x / 2 - 2 * (x + 2.39) ** (1 / 3)), 'x/2 - 2*(x + 2.39)^(1/3)'),
+ # https://cutt.ly/MzNdHH5
+ 4: Equation(lambda x: (-x / 2 + math.e ** x + 5 * math.sin(x)), '-x/2 + e^x + 5*sin(x)'),
+}
+
+ENABLE_LOGGING = True
+
+while True:
+ equation_type = mainboilerplate.choose_equation_type()
+
+ if equation_type == 1:
+ function = mainboilerplate.choose_equation(predefined_functions)
+
+ method_number = mainboilerplate.choose_method_number(methods)
+
+ while True:
+ if method_number == 4:
+ left, epsilon, decimal_places = mainboilerplate.read_initial_data_newton()
+ right = 0
+ else:
+ left, right, epsilon, decimal_places = mainboilerplate.read_initial_data()
+
+ method = methods[method_number](function, left, right, epsilon, decimal_places, ENABLE_LOGGING)
+ try:
+ verified, reason = method.check()
+ except TypeError as te:
+ print('(!) Ошибка при вычислении значения функции, возможно она не определена на всем интервале.')
+ continue
+ if verified:
+ break
+ else:
+ print('(!) Введенные исходные данные для метода некорректны: ', reason)
+
+ try:
+ function.draw(left, right)
+ except Exception as e:
+ print('(!) Не удалось построить график функции, ', e)
+
+ output_file_name = input("Введите имя файла для вывода результата или пустую строку, чтобы вывести в консоль: ")
+
+ try:
+ if ENABLE_LOGGING:
+ print('Процесс решения: ')
+ result = method.solve()
+ except Exception as e:
+ print(e)
+ print('(!) Что-то пошло не так при решении: ', e)
+ continue
+
+ mainboilerplate.print_result(result, output_file_name)
+
+ if input('\nЕще раз? [y/n] ') != 'y':
+ break
+ else:
+ system_of_equation.run()
diff --git a/4 вычмат/лабораторные/lab2/src/mainboilerplate.py b/4 вычмат/лабораторные/lab2/src/mainboilerplate.py
new file mode 100644
index 0000000..c352970
--- /dev/null
+++ b/4 вычмат/лабораторные/lab2/src/mainboilerplate.py
@@ -0,0 +1,112 @@
+from typing import Tuple
+import decimal
+
+from dto.equation import Equation
+
+def choose_equation_type():
+ print("Выберите тип программы:")
+ print('1: Нелинейное уравнение')
+ print('2: Система нелинейных уравнений')
+ try:
+ equation_type_number = int(input("Введите номер типа: "))
+ except ValueError:
+ print('(!) Вы ввели не число')
+ return choose_equation_type()
+ if equation_type_number != 1 and equation_type_number != 2:
+ print("(!) Такого номера нет.")
+ return choose_equation_type()
+ return equation_type_number
+
+
+def choose_equation(functions) -> Equation:
+ print("Выберите уравнение:")
+ for num, func in functions.items():
+ print(str(num) + ': ' + func.text)
+ try:
+ equation_number = int(input("Введите номер уравнения: "))
+ except ValueError:
+ print('(!) Вы ввели не число')
+ return choose_equation(functions)
+ if equation_number < 1 or equation_number > len(functions):
+ print("(!) Такого номера нет.")
+ return choose_equation(functions)
+ return functions[equation_number]
+
+
+def choose_method_number(methods) -> int:
+ print("Выберите метод:")
+ for num, mtd in methods.items():
+ print(str(num) + ': ' + mtd.name)
+ try:
+ method_number = int(input("Введите номер метода: "))
+ except ValueError:
+ print('(!) Вы ввели не число')
+ return choose_method_number(methods)
+ if method_number < 1 or method_number > len(methods):
+ print("(!) Такого номера нет.")
+ return choose_method_number(methods)
+ return method_number
+
+
+def print_result(result, output_file_name):
+ if output_file_name == '':
+ print('\n' + str(result))
+ else:
+ f = open(output_file_name, "w")
+ f.write(str(result))
+ f.close()
+ print('Результат записан в файл.')
+
+
+def read_initial_data() -> Tuple[float, float, float, int]:
+ while True:
+ filename = input("Введите имя файла для загрузки исходных данных и интервала "
+ "или пустую строку, чтобы ввести вручную: ")
+ if filename == '':
+ left = float(input('Введите левую границу интервала: '))
+ right = float(input('Введите правую границу интервала: '))
+ epsilon = input('Введите погрешность вычисления: ')
+ break
+ else:
+ try:
+ f = open(filename, "r")
+ left = float(f.readline())
+ right = float(f.readline())
+ epsilon = f.readline()
+ f.close()
+ print('Считано из файла:')
+ print(f'Левая граница: {left}, правая: {right}, погрешность: {epsilon}')
+ break
+ except FileNotFoundError:
+ print('(!) Файл для загрузки исходных данных не найден.')
+
+ decimal_places = abs(decimal.Decimal(epsilon).as_tuple().exponent)
+ epsilon = float(epsilon)
+
+ return left, right, epsilon, decimal_places
+
+
+def read_initial_data_newton() -> Tuple[float, float, int]:
+ while True:
+ filename = input("Введите имя файла для загрузки исходных данных и интервала "
+ "или пустую строку, чтобы ввести вручную: ")
+ if filename == '':
+ x0 = float(input('Введите начальное приближение: '))
+ epsilon = input('Введите погрешность вычисления: ')
+ break
+ else:
+ try:
+ f = open(filename, "r")
+ x0 = float(f.readline())
+ epsilon = f.readline()
+ f.close()
+ print('Считано из файла:')
+ print(f'Начальное приближение: {x0}, погрешность: {epsilon}')
+ break
+ except FileNotFoundError:
+ print('(!) Файл для загрузки исходных данных не найден.')
+
+ decimal_places = abs(decimal.Decimal(epsilon).as_tuple().exponent)
+ epsilon = float(epsilon)
+
+ return x0, epsilon, decimal_places
diff --git a/4 вычмат/лабораторные/lab2/src/methods/chord_method.py b/4 вычмат/лабораторные/lab2/src/methods/chord_method.py
new file mode 100644
index 0000000..fe99306
--- /dev/null
+++ b/4 вычмат/лабораторные/lab2/src/methods/chord_method.py
@@ -0,0 +1,42 @@
+import numpy as np
+
+from dto.result import Result
+from methods.method import Method
+
+class ChordMethod(Method):
+ name = 'Метод хорд'
+
+ def check(self):
+ root_exists = self.equation.root_exists(self.left, self.right)
+ return root_exists, 'Отсутствует корень на заданном промежутке' if not root_exists else ''
+
+ def solve(self) -> Result:
+ f = self.equation.function
+ a = self.left
+ b = self.right
+ epsilon = self.epsilon
+ iteration = 0
+
+ x = a - (b - a) * f(a) / (f(b) - f(a))
+
+ iteration = 0
+ last_x = x
+
+ while True:
+ if np.abs(f(x)) < epsilon:
+ break
+
+ iteration += 1
+
+ if f(a) * f(x) < 0:
+ b = x
+ else:
+ a = x
+
+ x = a - (b - a) * f(a) / (f(b) - f(a))
+ if self.log:
+ print(f'{iteration}: a = {a:.3f}, b = {b:.3f}, x = {x:.3f}, '
+ f'f(a) = {f(a):.3f}, f(b) = {f(b):.3f}, f(x)={f(x):.3f}, |x_k+1 - x_k| = {abs(x - last_x):.3f}')
+ last_x = x
+
+ return Result(x, f(x), iteration, self.decimal_places)
diff --git a/4 вычмат/лабораторные/lab2/src/methods/half_division_method.py b/4 вычмат/лабораторные/lab2/src/methods/half_division_method.py
new file mode 100644
index 0000000..4073d49
--- /dev/null
+++ b/4 вычмат/лабораторные/lab2/src/methods/half_division_method.py
@@ -0,0 +1,37 @@
+from dto.result import Result
+from methods.method import Method
+
+
+class HalfDivisionMethod(Method):
+ name = 'Метод половинного деления'
+
+ def check(self):
+ root_exists = self.equation.root_exists(self.left, self.right)
+ return root_exists, 'Отсутствует корень на заданном промежутке' if not root_exists else ''
+
+ def solve(self) -> Result:
+ f = self.equation.function
+ a = self.left
+ b = self.right
+ epsilon = self.epsilon
+
+ iteration = 0
+ while True:
+ iteration += 1
+ fa = f(a)
+ fb = f(b)
+ x = (a + b) / 2
+ fx = f(x)
+ if self.log:
+ print(f'{iteration}: a = {a:.3f}, b = {b:.3f}, x = {x:.3f}, '
+ f'f(a) = {fa:.3f}, f(b) = {fb:.3f}, f(x)={fx:.3f}, |a-b| = {abs(a - b):.3f}')
+
+ if abs(a - b) <= epsilon or abs(fx) <= epsilon:
+ break
+
+ if fa * fx < 0:
+ b = x
+ else:
+ a = x
+
+ return Result(x, fx, iteration, self.decimal_places)
diff --git a/4 вычмат/лабораторные/lab2/src/methods/method.py b/4 вычмат/лабораторные/lab2/src/methods/method.py
new file mode 100644
index 0000000..0b79039
--- /dev/null
+++ b/4 вычмат/лабораторные/lab2/src/methods/method.py
@@ -0,0 +1,23 @@
+from typing import Tuple
+
+from dto.equation import Equation
+from dto.result import Result
+
+
+class Method:
+ name = None
+
+ def __init__(self, equation: Equation, left: float, right: float,
+ epsilon: float, decimal_places: int, log: bool):
+ self.log = log
+ self.decimal_places = decimal_places
+ self.epsilon = epsilon
+ self.right = right
+ self.left = left
+ self.equation = equation
+
+ def solve(self) -> Result:
+ pass
+
+ def check(self) -> Tuple[bool, str]:
+ return True, ''
diff --git a/4 вычмат/лабораторные/lab2/src/methods/newton_method.py b/4 вычмат/лабораторные/lab2/src/methods/newton_method.py
new file mode 100644
index 0000000..7f97156
--- /dev/null
+++ b/4 вычмат/лабораторные/lab2/src/methods/newton_method.py
@@ -0,0 +1,33 @@
+import numpy as np
+from scipy.misc import derivative
+
+from dto.result import Result
+from methods.method import Method
+
+
+dx = 0.00001
+
+class NewtonMethod(Method):
+ name = 'Метод Ньютона'
+
+ def solve(self) -> Result:
+ f = self.equation.function
+ x0 = self.left
+
+ epsilon = self.epsilon
+ iteration = 0
+
+ while True:
+ iteration += 1
+
+ df = derivative(f, x0, dx=dx)
+ x1 = x0 - f(x0) / df
+ if self.log:
+ print(f'{iteration}: x_k = {x0:.3f}, f(x_k) = {f(x0):.3f}, '
+ f'f\'(x_k) = {df:.3f}, x_k+1 = {x1:.3f}, |x_k+1 - x_k| = {abs(x1 - x0)}')
+
+ if abs(x1 - x0) < epsilon:
+ break
+ x0 = x1
+
+ return Result(x1, f(x1), iteration, self.decimal_places)
diff --git a/4 вычмат/лабораторные/lab2/src/methods/simple_iterations_method.py b/4 вычмат/лабораторные/lab2/src/methods/simple_iterations_method.py
new file mode 100644
index 0000000..0dbefad
--- /dev/null
+++ b/4 вычмат/лабораторные/lab2/src/methods/simple_iterations_method.py
@@ -0,0 +1,53 @@
+import numpy
+from scipy.misc import derivative
+
+from dto.equation import Equation
+from dto.result import Result
+from methods.method import Method
+
+
+dx = 0.00001
+steps = 100
+
+class SimpleIterationsMethod(Method):
+ name = 'Метод простой итерации'
+
+ def __init__(self, equation: Equation, left: float, right: float,
+ epsilon: float, decimal_places: int, log: bool):
+ super().__init__(equation, left, right, epsilon, decimal_places, log)
+ f = self.equation.function
+ max_derivative = max(derivative(f, self.left, dx), derivative(f, self.right, dx))
+ _lambda = - 1 / max_derivative
+ self.phi = lambda x: x + _lambda * f(x)
+
+ def check(self):
+ if not self.equation.root_exists(self.left, self.right):
+ return False, 'Отсутствует корень на заданном промежутке'
+
+ # Достаточное условие сходимости метода |phi'(x)| < 1
+ print('phi\'(a) = ', abs(derivative(self.phi, self.left, dx)))
+ print('phi\'(b) = ', abs(derivative(self.phi, self.right, dx)))
+ for x in numpy.linspace(self.left, self.right, steps, endpoint=True):
+ if abs(derivative(self.phi, x, dx)) >= 1:
+ return False, 'Не выполнено условие сходимости метода |phi\'(x)| < 1 на интервале'
+ return True, ''
+
+ def solve(self) -> Result:
+ f = self.equation.function
+
+ prev = self.left
+
+ iteration = 0
+ while True:
+ iteration += 1
+ x = self.phi(prev)
+
+ diff = abs(x - prev)
+ if self.log:
+ print(f'{iteration}: xk = {prev:.3f}, f(xk) = {f(prev):.3f}, '
+ f'xk+1 = 𝜑(𝑥𝑘) = {x:.3f}, |xk - xk+1| = {diff:.3f}')
+
+ if diff <= self.epsilon:
+ break
+ prev = x
+ return Result(x, f(x), iteration, self.decimal_places)
diff --git a/4 вычмат/лабораторные/lab2/src/system_of_equation.py b/4 вычмат/лабораторные/lab2/src/system_of_equation.py
new file mode 100644
index 0000000..acadd02
--- /dev/null
+++ b/4 вычмат/лабораторные/lab2/src/system_of_equation.py
@@ -0,0 +1,80 @@
+from math import tan
+import numpy as np
+import matplotlib.pyplot as plt
+from scipy.optimize import fsolve
+
+def a(xy):
+ x, y = xy
+ return [x**2 + y**2 - 1, x**2 - y - 0.5]
+
+def b(xy):
+ x, y = xy
+ return [x**2 + y**2 - 1, x - y**2]
+
+def plot_system(system):
+ x = np.linspace(-2, 2, 400)
+ y = np.linspace(-2, 2, 400)
+ X, Y = np.meshgrid(x, y)
+
+ Z1 = np.array([system([x_, y_])[0] for x_, y_ in zip(np.ravel(X), np.ravel(Y))]).reshape(X.shape)
+ Z2 = np.array([system([x_, y_])[1] for x_, y_ in zip(np.ravel(X), np.ravel(Y))]).reshape(X.shape)
+
+ plt.contour(X, Y, Z1, levels=[0], colors='r')
+ plt.contour(X, Y, Z2, levels=[0], colors='b')
+ plt.xlabel('x')
+ plt.ylabel('y')
+ plt.show()
+
+def solve(system, x0, y0, epsilon, max_iter=1_000):
+ def jacobian(xy):
+ x, y = xy
+ return np.array([[2*x, 2*y], [2*x, -1]])
+
+ xy = np.array([x0, y0], dtype=float)
+ for i in range(max_iter):
+ J_inv = np.linalg.inv(jacobian(xy))
+ F = np.array(system(xy))
+ xy_next = xy - np.dot(J_inv, F)
+ error = np.linalg.norm(xy_next - xy)
+
+ if error < epsilon:
+ return xy_next, i + 1, error
+
+ xy = xy_next
+
+ raise Exception("Solution not found in {} iterations".format(max_iter))
+
+
+def choose_system_of_equations(functions):
+ print("Выберите систему уравнений:")
+ for key, value in functions.items():
+ print(str(key) + ": " + value[1])
+
+ try:
+ equations_number = int(input("Введите номер системы: "))
+ except ValueError:
+ print('(!) Вы ввели не число')
+ return choose_system_of_equations(functions)
+ if equations_number < 1 or equations_number > len(functions):
+ print("(!) Такого номера нет.")
+ return choose_system_of_equations(functions)
+ return functions[equations_number][0]
+
+def run():
+ systems = {1: [a, "x^2 + y^2 - 1, x^2 - y - 0.5"], 2: [b, "x^2 + y^2 - 1, x - y^2"]}
+ system = choose_system_of_equations(systems)
+
+ x0, y0 = map(float, input("Введите начальные приближения x0, y0: ").split())
+ epsilon = float(input('Введите погрешность вычисления: '))
+
+ xy_solution, iterations, error = solve(system, x0, y0, epsilon)
+
+ print(f"\nВектор неизвестных: x1 = {xy_solution[0]:.5f}, x2 = {xy_solution[1]:.5f}")
+ print(f"Количество итераций: {iterations}")
+ print(f"Вектор погрешностей: {error:.5e}")
+
+ residuals = np.abs(np.array(system(xy_solution)))
+ print("Проверка решения системы уравнений:")
+ print(f"Невязки: {residuals[0]:.5e}, {residuals[1]:.5e}\n")
+
+ plot_system(system)
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