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+ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + diff --git a/Л2-В6/Матвей/Form.py b/Л2-В6/Матвей/Form.py new file mode 100644 index 0000000..f8eb91d --- /dev/null +++ b/Л2-В6/Матвей/Form.py @@ -0,0 +1,205 @@ +import aim +import сomputational_mathematics as cm +from PyQt6.QtWidgets import QComboBox, QPushButton, QLineEdit, QFormLayout +import sys +import numpy as np +from PyQt6.QtWidgets import QApplication, QWidget, QVBoxLayout, QLabel +from PyQt6.QtGui import QIcon +from matplotlib.backends.backend_qt5agg import FigureCanvasQTAgg as FigureCanvas +from matplotlib.figure import Figure + + +class Form(QWidget): + def __init__(self): + super().__init__() + self.initUI() + + def initUI(self): + self.setWindowTitle("Lab2") + self.setWindowIcon(QIcon("icon.png")) + self.setGeometry(100, 100, 800, 940) + + main_layout = QVBoxLayout() + + # Группа "Уравнение" + equation_html = ( + 'Уравнение:' + ) + equation_html += "
" + equation_html += ( + 'y = x3 - 10 * x + 2' + ) + + # Создаем QLabel с использованием HTML разметки + label_equation = QLabel(self) + label_equation.setText(equation_html) + label_equation.setWordWrap(True) # Переносим текст если он не помещается в окне + + # Добавляем QLabel в вашу группу и на главный слой + group_equation = QVBoxLayout() + group_equation.addWidget(label_equation) + main_layout.addLayout(group_equation) + + # Группа "Параметры" + self.group_parameters = QFormLayout() + + label_name = QLabel("Параметры:", self) + label_name.setStyleSheet("color: rgb(87, 46, 120); font-size: 28px") + self.group_parameters.addWidget(label_name) + + self.label_a = QLabel("a:", self) + self.label_a.setStyleSheet("color: rgb(87, 46, 120); font-size: 20px") + self.line_edit_a = QLineEdit(self) + self.line_edit_a.setText("-10000.0") + + self.label_b = QLabel("b:", self) + self.label_b.setStyleSheet("color: rgb(87, 46, 120); font-size: 20px") + self.line_edit_b = QLineEdit(self) + self.line_edit_b.setText("10000.0") + + self.group_parameters.addRow(label_name) + self.group_parameters.addRow(self.label_a, self.line_edit_a) + self.group_parameters.addRow(self.label_b, self.line_edit_b) + main_layout.addLayout(self.group_parameters) + + # Группа "Действия" + self.group_actions = QVBoxLayout() + + label_actions = QLabel("Действия:", self) + label_actions.setStyleSheet("color: rgb(87, 46, 120); font-size: 28px") + + self.button_find_solution = QPushButton("Решить", self) + self.button_find_solution.clicked.connect(self.findSolution) + + self.combo_box_solutions = QComboBox(self) + self.combo_box_solutions.addItems( + [ + "Метод половинного деления", + "Метод хорд", + "Метод Ньютона", + "Модифицированный метод", + "Комбинированный метод", + "Итерационный метод", + ] + ) + + group_parameters = QFormLayout() + group_parameters.addRow(label_actions) + group_parameters.addRow(self.button_find_solution, self.combo_box_solutions) + + self.group_actions.addLayout(group_parameters) + + self.label_result = QLabel("Результат:", self) + self.label_result.setStyleSheet("color: rgb(87, 46, 120); font-size: 20px") + self.group_actions.addWidget(self.label_result) + + self.line_edit_result = QLineEdit(self) + self.group_actions.addWidget(self.line_edit_result) + + self.line_edit_roots = QLineEdit(self) + self.group_actions.addWidget(self.line_edit_roots) + + self.line_edit_section = QLineEdit(self) + self.group_actions.addWidget(self.line_edit_section) + + self.line_edit_result.setText(f"Решения: ") + self.line_edit_roots.setText(f"Найдено: z интервалов") + self.line_edit_section.setText(f"Отрезок (a, b)") + + main_layout.addLayout(self.group_actions) + + self.setLayout(main_layout) + + # Добавление виджета для графика + self.canvas = FigureCanvas(Figure()) + main_layout.addWidget(self.canvas) + + self.setLayout(main_layout) + self.plotGraph() + + def findSolution(self): + method = self.combo_box_solutions.currentText() + + a = float(self.line_edit_a.text()) + b = float(self.line_edit_b.text()) + + x_range = np.array(np.arange(a, b, step=0.1), dtype=np.float64) + y_range = aim.f(x_range) + + solution_range = [] + for i in range(len(x_range) - 1): + if y_range[i] * y_range[i + 1] < 0: + solution_range.append((x_range[i], x_range[i + 1])) + + strResult = "Решения: " + strSection = "Отрезки: " + + self.line_edit_roots.setText(f"Найдено: {len(solution_range)} интервала") + + for a, b in solution_range: + if method == "Метод половинного деления": + strResult += "[" + str(cm.half_div_method(aim.f, aim.f_d, a, b)) + "] " + strSection += f" ({a}, {b}) " + elif method == "Метод хорд": + strResult += ( + "[" + str(cm.chord_method(aim.f, aim.f_d, aim.f_dd, a, b)) + "] " + ) + strSection += f" ({a}, {b}) " + elif method == "Метод Ньютона": + strResult += "[" + str(cm.newtons_method(aim.f, aim.f_d, a, b)) + "] " + strSection += f" ({a}, {b}) " + elif method == "Модифицированный метод": + strResult += ( + "[" + str(cm.modified_newtons_method(aim.f, aim.f_d, a, b)) + "] " + ) + strSection += f" ({a}, {b}) " + elif method == "Комбинированный метод": + strResult += "[" + str(cm.combined_method(aim.f, aim.f_d, a, b)) + "] " + strSection += f" ({a}, {b}) " + elif method == "Итерационный метод": + strResult += "[" + str(cm.iterative_method(aim.f, aim.f_d, a, b)) + "] " + strSection += f" ({a}, {b}) " + + self.line_edit_section.setText(strSection) + self.line_edit_result.setText(strResult) + solution_range.clear() + + def plotGraph(self): + x = np.linspace(-10, 10, 400) + y = x**3 - 10 * x + 2 + ax = self.canvas.figure.subplots() + ax.plot(x, y, label="$x^3 - 10x + 2$", color="b") + + # Добавляем оси axis + ax.spines["left"].set_position(("data", 0)) + ax.spines["bottom"].set_position(("data", 0)) + ax.spines["right"].set_color("none") + ax.spines["top"].set_color("none") + ax.yaxis.set_ticks_position("left") + ax.xaxis.set_ticks_position("bottom") + + # Добавляем точки на оси x и их значения + x_intercepts = x[np.where(np.diff(np.signbit(y)))[0]] + for x_intercept in x_intercepts: + ax.plot(x_intercept, 0, "ro") # добавляем красную точку + ax.annotate( + f"x={x_intercept:.2f}", (x_intercept, 0.5), color="r" + ) # добавляем значение x + + # Ограничиваем график по оси y до 15 + ax.set_ylim(-15, 15) + + ax.set_title("График уравнения") + ax.set_xlabel("X") + ax.set_ylabel("Y") + ax.grid(True) + ax.legend() + + self.canvas.draw() + + +if __name__ == "__main__": + app = QApplication(sys.argv) + form = Form() + form.show() + sys.exit(app.exec()) diff --git a/Л2-В6/Матвей/aim.py b/Л2-В6/Матвей/aim.py new file mode 100644 index 0000000..3c2d966 --- /dev/null +++ b/Л2-В6/Матвей/aim.py @@ -0,0 +1,26 @@ +import sympy + +func_str = "x ** 3 - 10 * x + 2" +func = sympy.sympify(func_str) +func_d = sympy.diff(func) +func_dd = sympy.diff(func_d) + +func_l = sympy.lambdify("x", func, "numpy") +func_d_l = sympy.lambdify("x", func_d, "numpy") +func_dd_l = sympy.lambdify("x", func_dd, "numpy") + 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x_n + else: + a = x_n + i += 1 + return x_n + + +def chord_method(f, f_d, f_dd, a, b, max_iter=1_000_000, eps=0.01): + x_n = (a + b) / 2 + i = 0 + while abs(f(x_n)) >= eps and i < max_iter: + X = a + if f(X) * f_dd(X) <= 0: + X = b + if f(X) * f_dd(X) <= 0: + return None + + x_n = x_n - f(x_n) * (X - x_n) / (f(X) - f(x_n)) + i += 1 + + return x_n + + +def newtons_method(f, f_d, a, b, max_iter=10_000, eps=0.00001): + x_n = a + i = 0 + while abs(f(x_n)) >= eps and i < max_iter: + x_n = x_n - f(x_n) / f_d(x_n) + i += 1 + return x_n + + +def modified_newtons_method(f, f_d, a, b, max_iter=1_000_000, eps=0.01): + x_n = a + f_d_0 = f_d(x_n) + i = 0 + + while abs(f(x_n)) >= eps and i < max_iter: + x_n = x_n - f(x_n) / f_d_0 + i += 1 + return x_n + + +def combined_method(f, f_d, a, b, max_iter=10_000, eps=0.00001): + x_n = a + y_n = b + i = 0 + + while abs(x_n - y_n) >= eps and i < max_iter: + x_n = x_n - f(x_n) / f_d(x_n) + y_n = y_n - f(y_n) * (x_n - y_n) / (f(x_n) - f(y_n)) + i += 1 + return 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@@ -0,0 +1,2 @@ +.venv +*/__pycache__ \ No newline at end of file diff --git a/Л2-В6/Программа/requirements.txt b/Л2-В6/Программа/requirements.txt new file mode 100644 index 0000000..d0bc151 --- /dev/null +++ b/Л2-В6/Программа/requirements.txt @@ -0,0 +1,5 @@ +sympy +numpy +matplotlib +pyqt6 +scipy \ No newline at end of file diff --git a/Л2-В6/Программа/src/algorithm.py b/Л2-В6/Программа/src/algorithm.py new file mode 100644 index 0000000..8aa7e8e --- /dev/null +++ b/Л2-В6/Программа/src/algorithm.py @@ -0,0 +1,82 @@ +def half_div_method(f, a, b, max_iter=10_000, eps=0.00001): + x_n = (a + b) / 2 + i = 0 + while abs(f(x_n)) >= eps and i < max_iter: + x_n = (a + b) / 2 + + if f(a) * f(x_n) < 0: + b = x_n + else: + a = x_n + + i += 1 + + return x_n + + +def chord_method(f, f_dd, a, b, max_iter=10_000, eps=0.00001): + x_n = (a + b) / 2 + i = 0 + while abs(f(x_n)) >= eps and i < max_iter: + X = a + if f(X) * f_dd(X) <= 0: + X = b + if f(X) * f_dd(X) <= 0: + return None + + x_n = x_n - f(x_n) * (X - x_n) / (f(X) - f(x_n)) + + i += 1 + + return x_n + + +def newtons_method(f, f_d, a, b, max_iter=10_000, eps=0.00001): + x_n = a + i = 0 + while abs(f(x_n)) >= eps and i < max_iter: + x_n = x_n - f(x_n) / f_d(x_n) + + i += 1 + + return x_n + + +def modified_newtons_method(f, f_d, a, b, max_iter=10_000, eps=0.00001): + x_n = a + f_d_0 = f_d(x_n) + + i = 0 + while abs(f(x_n)) >= eps and i < max_iter: + x_n = x_n - f(x_n) / f_d_0 + + i += 1 + + return x_n + + +def combined_method(f, f_d, a, b, max_iter=10_000, eps=0.00001): + x_n = a + y_n = b + i = 0 + while abs(x_n - y_n) >= eps and i < max_iter: + x_n = x_n - f(x_n) / f_d(x_n) + y_n = y_n - f(y_n) * (x_n - y_n) / (f(x_n) - f(y_n)) + + i += 1 + + return (x_n + y_n) / 2 + + +def iterative_method(f, f_d, a, b, max_iter=10_000, eps=0.0001): + def phi(x): + return x - f(x) / f_d(x) + + x = phi(a) + i = 0 + while abs(f(x)) >= eps and i < max_iter: + x = phi(x) + + i += 1 + + return x diff --git a/Л2-В6/Программа/src/main.py b/Л2-В6/Программа/src/main.py new file mode 100644 index 0000000..06cb41f --- /dev/null +++ b/Л2-В6/Программа/src/main.py @@ -0,0 +1,13 @@ +import sys +from PyQt6.QtWidgets import QApplication +from PyQt6.QtGui import QFont + +import window + +if __name__ == "__main__": + app = QApplication(sys.argv) + font = QFont("Cascadia Code", 14) + app.setFont(font) + window = window.MainWindow() + window.show() + sys.exit(app.exec()) diff --git a/Л2-В6/Программа/src/task.py b/Л2-В6/Программа/src/task.py new file mode 100644 index 0000000..480ee42 --- /dev/null +++ b/Л2-В6/Программа/src/task.py @@ -0,0 +1,27 @@ +import sympy + +func_str = "x ** 4 - x ** 2 + 5 * x - 10" + +func = sympy.sympify(func_str) +func_d = sympy.diff(func) +func_dd = sympy.diff(func_d) + +func_l = sympy.lambdify("x", func, cse=True) +func_d_l = sympy.lambdify("x", func_d, cse=True) +func_dd_l = sympy.lambdify("x", func_dd, cse=True) + + +def f_str(): + return func_str + + +def f(x): + return func_l(x) + + +def f_d(x): + return func_d_l(x) + + +def f_dd(x): + return func_dd_l(x) diff --git a/Л2-В6/Программа/src/window.py b/Л2-В6/Программа/src/window.py new file mode 100644 index 0000000..fd9848e --- /dev/null +++ b/Л2-В6/Программа/src/window.py @@ -0,0 +1,232 @@ +import task +from algorithm import * + +import sys +from PyQt6.QtWidgets import ( + QMessageBox, + QMainWindow, + QLabel, + QComboBox, + QPushButton, + QFormLayout, + QWidget, + QLineEdit, + QHBoxLayout, +) +from PyQt6.QtCore import Qt +import numpy as np +import scipy + +import matplotlib +import matplotlib.pyplot as plt +from matplotlib.backends.backend_qt5agg import FigureCanvasQTAgg + +matplotlib.use("QtAgg") + + +class InputField(QWidget): + def __init__(self, parent, label_text, placeholder_text, lineedit_text): + super().__init__(parent) + + self._layout = QHBoxLayout(self) + self._layout.setContentsMargins(0, 0, 0, 0) + self.label = QLabel(label_text) + self.lineedit = QLineEdit(lineedit_text) + self.lineedit.setPlaceholderText(placeholder_text) + + self._layout.addWidget(self.label) + self._layout.addWidget(self.lineedit) + + def get_value(self): + return self.lineedit.text() + + def set_value(self, value): + self.lineedit.setText(value) + + def on_change(self, func): + self.lineedit.textChanged.connect(func) + + +class MainWindow(QMainWindow): + def __init__(self): + super().__init__() + + self.a = float(-3) + self.b = float(2) + self.steps = int(1000) + + self.setupUI() + + def setupUI(self): + self.setWindowTitle("Лабораторная работа №2") + self.setFixedSize(800, 800) + + self.central_widget = QWidget() + self.setCentralWidget(self.central_widget) + + layout = QFormLayout() + + self.label1 = QLabel("Вариант 6", self) + layout.addWidget(self.label1) + self.label5 = QLabel(f"Уравнение {task.f_str()}", self) + layout.addWidget(self.label5) + + self.label3 = QLabel("Диапазон:", self) + layout.addWidget(self.label3) + + self.aInput = InputField(self, " a: ", "от", str(self.a)) + self.aInput.on_change(self.aInput_changed) + layout.addWidget(self.aInput) + + self.bInput = InputField(self, " b: ", "до", str(self.b)) + self.bInput.on_change(self.bInput_changed) + layout.addWidget(self.bInput) + + self.stepsInput = InputField(self, " шаги: ", "шаги", str(self.steps)) + self.stepsInput.on_change(self.stepsInput_changed) + layout.addWidget(self.stepsInput) + + self.plot = plt.figure() + self.canvas = FigureCanvasQTAgg(self.plot) + self.plot_axes = self.plot.add_subplot(111) + self.drawPlot(self.a, self.b) + layout.addWidget(self.canvas) + + self.findIntervalsButton = QPushButton("Найти интервалы", self) + self.findIntervalsButton.clicked.connect(self.findIntervalsButton_clicked) + layout.addWidget(self.findIntervalsButton) + + self.intervals = [] + self.comboBoxIntervals = QComboBox(self) + layout.addWidget(self.comboBoxIntervals) + + self.label2 = QLabel("Способ решения:", self) + layout.addWidget(self.label2) + + self.comboBoxSolutions = QComboBox(self) + self.comboBoxSolutions.addItem("Половинного деления") + self.comboBoxSolutions.addItem("Хорд") + self.comboBoxSolutions.addItem("Ньютона") + self.comboBoxSolutions.addItem("Ньютона (мод)") + self.comboBoxSolutions.addItem("Комбинированный") + self.comboBoxSolutions.addItem("Итераций") + layout.addWidget(self.comboBoxSolutions) + + self.buttonFindSolution = QPushButton("Решить", self) + self.buttonFindSolution.clicked.connect(self.findSolutionButton_clicked) + layout.addWidget(self.buttonFindSolution) + + self.label4 = QLabel("Ответ:", self) + layout.addWidget(self.label4) + + self.labelResult = QLabel(self) + layout.addWidget(self.labelResult) + + self.central_widget.setLayout(layout) + + def aInput_changed(self): + try: + a_str = self.aInput.get_value() + if not (a_str == "" or a_str == "-"): + self.a = float(a_str) + self.drawPlot(self.a, self.b) + except: + self.aInput.set_value(str(self.a)) + + def bInput_changed(self): + try: + b_str = self.bInput.get_value() + if not (b_str == "" or b_str == "-"): + self.b = float(b_str) + self.drawPlot(self.a, self.b) + except: + self.bInput.set_value(str(self.b)) + + def stepsInput_changed(self): + try: + steps_str = self.stepsInput.get_value() + if not (steps_str == ""): + self.steps = int(steps_str) + self.steps = max(2, min(10000, self.steps)) + self.stepsInput.set_value(str(self.steps)) + self.drawPlot(self.a, self.b) + except: + self.stepsInput.set_value(str(self.steps)) + + def redraw(self): + self.canvas.draw() + + def findIntervalsButton_clicked(self): + self.intervals = self.find_root_intervals( + self.a, self.b, abs(self.b - self.a) / self.steps, task.f + ) + self.comboBoxIntervals.clear() + for a, b in self.intervals: + self.comboBoxIntervals.addItem(f"({a:.5f}, {b:.5f})") + + def findSolutionButton_clicked(self): + try: + (a, b) = self.intervals[self.comboBoxIntervals.currentIndex()] + solution = self.find_root(a, b, self.comboBoxSolutions.currentIndex()) + + if solution is None: + self.labelResult.setText("Решение не найдено") + else: + self.labelResult.setText(f"{solution:.12f}") + except: + self.labelResult.setText("Интервал не выбран") + + def drawPlot(self, a, b): + steps = self.steps + step = abs(b - a) / steps + + intervals = self.find_root_intervals(a, b, step, task.f) + roots = [] + for interval in intervals: + root = scipy.optimize.fsolve(task.f, interval) + roots.extend(root) + + x_values = np.linspace(a, b, steps) + y_values = task.f(x_values) + ax = self.plot_axes + ax.clear() + ax.plot(x_values, y_values) + ax.axhline(0, color="black", linewidth=1) + ax.set_xlabel("x") + ax.axvline(0, color="black", linewidth=1) + ax.set_ylabel("y") + ax.grid(True) + ax.plot(x_values, y_values, label="y = f(x)") + + ax.scatter(roots, np.zeros_like(roots), color="red") + for root in roots: + ax.text(root, 0, f"x={root:.5f}", ha="left", va="bottom") + + self.redraw() + + def find_root(self, a, b, method): + solution = None + match method: + case 0: + solution = half_div_method(task.f, a, b) + case 1: + solution = chord_method(task.f, task.f_dd, a, b) + case 2: + solution = newtons_method(task.f, task.f_d, a, b) + case 3: + solution = modified_newtons_method(task.f, task.f_d, a, b) + case 4: + solution = combined_method(task.f, task.f_d, a, b) + case 5: + solution = iterative_method(task.f, task.f_d, a, b) + + return solution + + def find_root_intervals(self, a, b, step, f): + x_range = np.array(np.arange(a, b, step), dtype=np.float64) + y_range = f(x_range) + solution_range = [] + for i in range(len(x_range) - 1): + if y_range[i] * y_range[i + 1] < 0: + solution_range.append((x_range[i], x_range[i + 1])) + return solution_range diff --git a/Л3-В6/Lab_3.pdf b/Л3-В6/Lab_3.pdf new file mode 100644 index 0000000000000000000000000000000000000000..31ef20c93ab8e54c07e04c3066a254b8dc22d455 GIT binary patch literal 463810 zcmc$`bF6N`vadaDtZ8da+qP}2Y1_7K+qP}nwr!ht?S0NZxViam&L1~lGLkn{-BsO{ 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