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Suiranoil
2024-03-19 14:03:49 +03:00
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<mxGeometry relative="1" as="geometry" />
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<mxCell id="G-ayLxhA-LWAzPQ1L_Mv-14" value="return x" style="rounded=0;whiteSpace=wrap;html=1;" vertex="1" parent="1">
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<mxCell id="JN9VUWSohEjc5PBiCDA9-1" value="Да" style="text;html=1;align=center;verticalAlign=middle;resizable=0;points=[];autosize=1;strokeColor=none;fillColor=none;" vertex="1" parent="1">
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<mxCell id="JN9VUWSohEjc5PBiCDA9-2" value="Нет" style="text;html=1;align=center;verticalAlign=middle;resizable=0;points=[];autosize=1;strokeColor=none;fillColor=none;" vertex="1" parent="1">
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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())

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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)

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Л2-В6/Матвей/сomputational_mathematics.py Normal file
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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

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.venv
*/__pycache__

5
Л2-В6/Программа/requirements.txt Normal file
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sympy
numpy
matplotlib
pyqt6
scipy

82
Л2-В6/Программа/src/algorithm.py Normal file
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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

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Л2-В6/Программа/src/main.py Normal file
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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())

27
Л2-В6/Программа/src/task.py Normal file
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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)

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Л2-В6/Программа/src/window.py Normal file
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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