first commit

Л2-В6/Матвей/Form.py

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+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 = (
+            '<span style="color:rgb(87, 46, 120); font-size:28px;">Уравнение:</span>'
+        )
+        equation_html += "<br>"
+        equation_html += (
+            '<span style="font-size:28px;">y = x<sup>3</sup> - 10 * x + 2</span>'
+        )
+
+        # 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())

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")
+
+
+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)

Л2-В6/Матвей/сomputational_mathematics.py

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+def half_div_method(f, f_d, 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
+
+        f_ = f(x_n)
+        if f_ == 0:
+            break
+
+        if f(a) * f_ < 0:
+            b = 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 (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)
+
+    i = 0
+    x = phi(a)
+
+    while abs(f(x)) >= eps and i < max_iter:
+        x = phi(x)
+        i += 1
+    return x