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4 Commits
cc4c61bc4d ... main

Author SHA1 Message Date
lionarius
fe726bd935 lab5 2024-05-05 20:42:32 +03:00
lionarius
7513fe88cf lab4 qol 2024-04-22 05:38:36 +03:00
lionarius
b4d255e19b Merge branch 'main' of https://gitea.lionarius.ru/lionarius/computational-math 2024-04-22 01:05:09 +03:00
lionarius
70c7975eeb lab4 2024-04-22 01:04:56 +03:00
20 changed files with 2177 additions and 0 deletions
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Л4-В6/Lab_4.pdf Normal file
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Л4-В6/Блоксхема.drawio Normal file
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Л4-В6/Программа/.gitignore vendored Normal file
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.venv
*/__pycache__

5
Л4-В6/Программа/requirements.txt Normal file
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sympy
numpy
scipy
pyqt6
matplotlib

60
Л4-В6/Программа/src/algorithm.py Normal file
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import numpy as np
import typing
def difference_n(
func: typing.Callable[[float], float], x_array: np.ndarray, start: int, end: int
) -> float:
if len(x_array) < end + 1:
return None
result = 0
for k in range(start, end + 1):
prod = 1
for j in range(start, end + 1):
if j != k:
prod *= x_array[k] - x_array[j]
result += func(x_array[k]) / prod
return result
def make_forward_interpolate_function(
func: typing.Callable[[float], float], x_array: np.ndarray
) -> typing.Callable[[float], float]:
n = len(x_array)
diffs = [difference_n(func, x_array, 0, k) for k in range(1, n)]
def forward_interpolate(x: float) -> float:
L = func(x_array[0])
for k in range(1, n):
prod = diffs[k - 1]
for i in range(k):
prod *= x - x_array[i]
L += prod
return L
return forward_interpolate
def make_backward_interpolate_function(
func: typing.Callable[[float], float], x_array: np.ndarray
) -> typing.Callable[[float], float]:
n = len(x_array)
diffs = [difference_n(func, x_array, n - k - 1, n - 1) for k in range(1, n)]
def backward_interpolate(x: float) -> float:
L = func(x_array[-1])
for k in range(n - 1):
prod = diffs[k]
for i in range(n - 1, n - k - 2, -1):
prod *= x - x_array[i]
L += prod
return L
return backward_interpolate

14
Л4-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())

10
Л4-В6/Программа/src/task.py Normal file
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func_str = "exp(-b * x) * cos(pi * (x + x ** 2))"
func_args = {"b": 0.15}
def f_str() -> str:
return func_str
def f_args() -> dict:
return func_args.copy()

219
Л4-В6/Программа/src/widgets.py Normal file
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from PyQt6.QtWidgets import (
QLabel,
QWidget,
QLineEdit,
QHBoxLayout,
QSlider,
)
from PyQt6.QtCore import Qt
import abc
import typing
class DisplayField(QWidget):
label_text: str
def __init__(self, parent, label_text="", text=""):
super().__init__(parent)
self._layout = QHBoxLayout(self)
self._layout.setContentsMargins(0, 0, 0, 0)
self.label_text = label_text
self.text = QLabel(f"{self.label_text}{text}")
self.text.setAlignment(Qt.AlignmentFlag.AlignLeft)
self._layout.addWidget(self.text)
def set_visible(self, visible):
self.text.setVisible(visible)
def set_text(self, text):
self.text.setText(f"{self.label_text}{text}")
class InputWidget(QWidget):
value: typing.Any
previous_value: typing.Any
callback: typing.Callable[[typing.Self], bool] | None = None
def init(self):
self.value = self._get_value_internal()
self.previous_value = self.value
self._set_callback_internal(self._on_change_internal)
def get_value(self) -> typing.Any:
return self.value
def get_previous_value(self) -> typing.Any:
return self.previous_value
def set_value(self, value: typing.Any):
self._set_value_internal(value)
self._set_value_no_sync(value)
def set_callback(self, callback: typing.Callable[[typing.Self], bool]):
self.callback = callback
@abc.abstractmethod
def _get_value_internal(self) -> typing.Any:
pass
@abc.abstractmethod
def _set_value_internal(self, value: typing.Any):
pass
@abc.abstractmethod
def _set_callback_internal(self, callback: typing.Callable[[], None]):
pass
def _set_value_no_sync(self, value: typing.Any):
self.previous_value = self.value
self.value = value
def _on_change_internal(self):
self._set_value_no_sync(self._get_value_internal())
if self.callback:
self.callback(self)
def make_callback_chain(
callbacks: typing.List[typing.Callable[[InputWidget], bool]]
) -> typing.Callable[[InputWidget], bool]:
def callback(widget: InputWidget):
for callback in callbacks:
if not callback(widget):
break
return True
return callback
def make_min_max_callback(
min: typing.Any, max: typing.Any
) -> typing.Callable[[InputWidget], bool]:
def callback(widget: InputWidget):
value = widget.get_value()
if type(min)(value) < min:
widget.set_value(min)
if type(max)(value) > max:
widget.set_value(max)
return True
return callback
def float_check_callback(widget: InputWidget):
try:
internal_value = widget._get_value_internal()
if not (internal_value == "" or internal_value == "-" or internal_value == "."):
_ = float(widget.get_value())
return True
else:
widget.value = widget.previous_value
return False
except:
widget.set_value(widget.previous_value)
return False
def int_check_callback(widget: InputWidget):
try:
internal_value = widget._get_value_internal()
if not (internal_value == "" or internal_value == "-"):
_ = int(widget.get_value())
return True
else:
widget.value = widget.previous_value
return False
except:
widget.set_value(widget.previous_value)
return False
class InputField(InputWidget):
def __init__(
self,
parent,
label_text="",
placeholder_text="",
lineedit_text="",
label_position="left",
):
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.lineedit.setMinimumWidth(50)
if label_position == "left":
self._layout.addWidget(self.label)
self._layout.addWidget(self.lineedit)
elif label_position == "right":
self._layout.addWidget(self.lineedit)
self._layout.addWidget(self.label)
elif label_position == "none":
self._layout.addWidget(self.lineedit)
super().init()
super().set_value(lineedit_text)
def _get_value_internal(self):
return self.lineedit.text()
def _set_value_internal(self, value):
self.lineedit.setText(str(value))
def _set_callback_internal(self, callback):
self.lineedit.textChanged.connect(callback)
class InputSlider(InputWidget):
slider: QSlider
def __init__(
self,
parent,
label_text="",
value=0,
min_value=0,
max_value=100,
step=1,
ticks=False,
):
super().__init__(parent)
self._layout = QHBoxLayout(self)
self._layout.setContentsMargins(0, 0, 0, 0)
self.label = QLabel(label_text)
self.slider = QSlider(Qt.Orientation.Horizontal)
if ticks:
self.slider.setTickPosition(QSlider.TickPosition.TicksBelow)
self.slider.setTickInterval(step)
self.slider.setMinimum(min_value)
self.slider.setMaximum(max_value)
self.slider.setValue(value)
self.slider.setSingleStep(step)
self._layout.addWidget(self.label)
self._layout.addWidget(self.slider)
super().init()
super().set_value(value)
def _get_value_internal(self):
return self.slider.value()
def _set_value_internal(self, value):
self.slider.setValue(value)
def _set_callback_internal(self, callback):
self.slider.valueChanged.connect(callback)

588
Л4-В6/Программа/src/window.py Normal file
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from PyQt6.QtWidgets import (
QMainWindow,
QLabel,
QPushButton,
QFormLayout,
QWidget,
QHBoxLayout,
)
from PyQt6 import QtWidgets
import numpy as np
import sympy
from typing import *
import matplotlib
import matplotlib.pyplot as plt
from matplotlib.figure import Figure
from matplotlib.axes import Axes
from matplotlib.backends.backend_qtagg import FigureCanvasQTAgg
matplotlib.use("QtAgg")
import widgets
import task
import algorithm
class ParamsField(widgets.InputWidget):
_layout: QFormLayout
fields: Dict[str, widgets.InputWidget]
callback_internal: Callable
def __init__(self, parent, fields: List[str]):
super().__init__(parent)
self._initialize()
self._create(fields)
super().init()
def _initialize(self):
self.fields = {}
self._layout = QFormLayout(self)
self._layout.setContentsMargins(0, 0, 0, 0)
def _create(self, fields: List[str]):
fields = sorted(fields)
for field in fields:
val = "0.0"
if not self.value.get(field) is None:
val = str(self.value.get(field))
self.fields[field] = widgets.InputField(
self, label_text=f"{field:>4}: ", lineedit_text=val
)
self.fields[field].set_callback(
widgets.make_callback_chain(
[widgets.float_check_callback, self._callback]
)
)
self._layout.addRow(self.fields[field])
def recreate(self, fields: List[str]):
for field in self.fields:
self.fields[field].deleteLater()
self.fields = {}
self._create(fields)
self.callback_internal()
def _get_value_internal(self) -> Dict[str, float]:
value = {}
for field in self.fields:
value[field] = float(self.fields[field].get_value())
return value
def _set_value_internal(self, value: Dict[str, float]):
for field in self.fields:
self.fields[field].set_value(value[field])
def _set_callback_internal(self, callback):
self.callback_internal = callback
def _callback(self, widget: widgets.InputWidget):
self.callback_internal()
return True
class PointsField(widgets.InputWidget):
_layout: QFormLayout
points: List[widgets.InputField]
min: float
max: float
DIVISIONS = 1_000_000
callback_internal: Callable[[None], None]
def __init__(self, parent, start: int, points: List[float], min: float, max: float):
super().__init__(parent)
self._initialize()
self._create(start, points, min, max)
super().init()
def _initialize(self):
self.points = []
self.min = 0.0
self.max = 1.0
self._layout = QFormLayout(self)
self._layout.setContentsMargins(0, 0, 0, 0)
def _create(self, start: int, points: List[float], min: float, max: float):
self.min = min
self.max = max
for i in range(0, len(points)):
value = int((points[i] - min) / (max - min) * self.DIVISIONS)
self.points.append(
widgets.InputSlider(
self,
label_text=f"{i + start:>4}: ",
value=value,
min_value=0,
max_value=self.DIVISIONS,
)
)
self.points[i].set_callback(
widgets.make_callback_chain(
[widgets.float_check_callback, self._callback]
)
)
self._layout.addRow(self.points[i])
def recreate(self, start: int, points: List[float], min: float, max: float):
for point in self.points:
point.deleteLater()
self.points = []
self._create(start, points, min, max)
self.callback_internal()
def _get_value_internal(self) -> List[float]:
value = []
for point in self.points:
value.append(
float(point.get_value()) / self.DIVISIONS * (self.max - self.min)
+ self.min
)
return value
def _set_value_internal(self, value: List[float]):
for i in range(0, len(value)):
self.points[i].set_value(
(value[i] - self.min) / (self.max - self.min) * self.DIVISIONS
)
def _set_callback_internal(self, callback):
self.callback_internal = callback
def _callback(self, widget: widgets.InputWidget):
self.callback_internal()
return True
class PlotWidget(QWidget):
figure: Figure
axes: Axes
canvas: FigureCanvasQTAgg
pre_style: Callable[[Axes], None]
post_style: Callable[[Axes], None]
plots: List[Callable[[Axes], None]]
def __init__(self, parent):
super().__init__(parent)
self._layout = QHBoxLayout(self)
self.figure = plt.figure()
self.axes = self.figure.add_subplot(111)
self.figure.tight_layout(pad=3)
self.figure.subplots_adjust(left=0.15, right=0.975, top=0.95)
self.figure.patch.set_facecolor("#f0f0f0")
self.canvas = FigureCanvasQTAgg(self.figure)
self._layout.addWidget(self.canvas)
self.pre_style = lambda _: None
self.plots = []
def set_pre_style(self, style: Callable[[Axes], None]):
self.pre_style = style
def set_post_style(self, style: Callable[[Axes], None]):
self.post_style = style
def clear_plots(self):
self.plots = []
def add_plot(self, plot: Callable[[Axes], None]):
self.plots.append(plot)
def redraw(self):
self.axes.clear()
self.pre_style(self.axes)
for plot in self.plots:
plot(self.axes)
self.post_style(self.axes)
self.canvas.draw()
class MainWindow(QMainWindow):
central_widget: QWidget
function_field: widgets.InputField
function_param_fields: ParamsField
x_0_field: widgets.InputField
x_n_field: widgets.InputField
n_display: widgets.DisplayField
n_slider: widgets.InputSlider
points_field: PointsField
margin_display: widgets.DisplayField
margin_slider: widgets.InputSlider
function_plot: PlotWidget
error_plot: PlotWidget
function: Callable[[float], float]
interpolated_function: Callable[[float], float]
function_params: Dict[str, float]
x_0: float
x_n: float
n: int
points: List[float]
margin: float
parsing_function: bool
updating: bool
def __init__(self):
super().__init__()
self.n = 2
self.margin = 5
self.x_0 = 0.0
self.x_n = 1.0
self.points = [0.5]
self.function = None
self.function_params = {}
self.parsing_function = False
self.setup_ui()
self.reset()
def setup_ui(self):
self.setWindowTitle("Лабораторная работа №4")
self.setFixedSize(1400, 800)
self.central_widget = QWidget(self)
self.setCentralWidget(self.central_widget)
layout = QHBoxLayout(self.central_widget)
left_row = QWidget(self.central_widget)
left_row_layout = QFormLayout(left_row)
right_row = QWidget(self.central_widget)
right_row_layout = QFormLayout(right_row)
self.function_field = widgets.InputField(self, label_text="Функция: ")
self.function_field.set_callback(self._function_field_changed)
left_row_layout.addWidget(self.function_field)
self.function_param_fields = ParamsField(self, [])
self.function_param_fields.set_callback(self._function_param_field_changed)
left_row_layout.addWidget(self.function_param_fields)
self.x_0_field = widgets.InputField(
self, label_text="x_0: ", lineedit_text="0.0"
)
self.x_0_field.set_callback(
widgets.make_callback_chain(
[widgets.float_check_callback, self._x_0_field_changed]
)
)
left_row_layout.addWidget(self.x_0_field)
self.x_n_field = widgets.InputField(
self, label_text="x_n: ", lineedit_text="1.0"
)
self.x_n_field.set_callback(
widgets.make_callback_chain(
[widgets.float_check_callback, self._x_n_field_changed]
)
)
left_row_layout.addWidget(self.x_n_field)
self.n_display = widgets.DisplayField(self, "n: ", "")
left_row_layout.addWidget(self.n_display)
self.n_slider = widgets.InputSlider(self, "", 1, 1, 20, 1, True)
self.n_slider.set_callback(self._n_slider_changed)
left_row_layout.addWidget(self.n_slider)
self.points_field = PointsField(self, 1, [0.5], 0.0, 1.0 - 0.001)
self.points_field.set_callback(self._points_field_changed)
left_row_layout.addWidget(self.points_field)
self.margin_display = widgets.DisplayField(self, "отступ (%): ", "")
left_row_layout.addWidget(self.margin_display)
self.margin_slider = widgets.InputSlider(self, "", 5, 1, 500, 1)
self.margin_slider.set_callback(self._margin_slider_changed)
left_row_layout.addWidget(self.margin_slider)
reset_button = QPushButton("Сброс", self)
reset_button.clicked.connect(self.reset)
left_row_layout.addWidget(reset_button)
label1 = QLabel("График функции", self)
right_row_layout.addWidget(label1)
self.function_plot = PlotWidget(self)
self.function_plot.set_pre_style(self.function_plot_pre_style)
self.function_plot.set_post_style(self.function_plot_post_style)
right_row_layout.addWidget(self.function_plot)
label2 = QLabel("График ошибки", self)
right_row_layout.addWidget(label2)
self.error_plot = PlotWidget(self)
self.error_plot.set_pre_style(self.function_plot_pre_style)
self.error_plot.set_post_style(self.function_plot_post_style)
right_row_layout.addWidget(self.error_plot)
left_row.setLayout(left_row_layout)
right_row.setLayout(right_row_layout)
layout.addWidget(left_row)
layout.addWidget(right_row)
self.central_widget.setLayout(layout)
def function_plot_pre_style(self, axes: Axes):
axes.set_xlabel("x")
axes.set_ylabel("y")
axes.axhline(0, color="black", linewidth=1)
axes.axvline(0, color="black", linewidth=1)
axes.grid(True)
def function_plot_post_style(self, axes: Axes):
axes.legend(loc="upper left")
def reset(self):
self.function_field.set_value(task.f_str())
self.x_0_field.set_value(0.0)
self.x_n_field.set_value(1.0)
self.n_slider.set_value(5)
self.margin_slider.set_value(300)
QtWidgets.QApplication.processEvents()
self.function_params = task.f_args()
self.function_param_fields.set_value(self.function_params)
QtWidgets.QApplication.processEvents()
self.redraw_plots()
QtWidgets.QApplication.processEvents()
def redraw_plots(self):
length = abs(self.x_n - self.x_0)
x_margin = length / 2 * self.margin
x_min = self.x_0 - x_margin
x_max = self.x_n + x_margin
visible_length = abs(x_max - x_min)
plot_x_margin = visible_length / 2 * 0.025
steps = max(
min(int(500 * 1 / visible_length**1.1), 5000),
min(int(750 * visible_length**1.5), 10000),
)
x_values = np.linspace(x_min, x_max, steps)
y_values = self.function(x_values)
y_interpolated = self.interpolated_function(x_values)
self.function_plot.clear_plots()
self.function_plot.add_plot(
lambda axes: axes.set_xlim(x_min - plot_x_margin, x_max + plot_x_margin)
)
self.function_plot.add_plot(
lambda axes: axes.plot(x_values, y_values, label="y = f(x)", color="red")
)
self.function_plot.add_plot(
lambda axes: axes.plot(
x_values,
y_interpolated,
label="y = L(x)",
color="blue",
linestyle="dashed",
)
)
points = [self.x_0, self.x_n]
points[1:1] = self.points
points = np.array(points)
self.function_plot.add_plot(
lambda axes: axes.scatter(
points, self.function(points), color="green", zorder=10
)
)
def label_func(axes):
for i in range(len(points)):
axes.text(
points[i],
self.function(points[i]) + 0.05,
str(i),
ha="center",
va="bottom",
color="green",
)
self.function_plot.add_plot(label_func)
self.error_plot.clear_plots()
self.error_plot.add_plot(
lambda axes: axes.set_xlim(x_min - plot_x_margin, x_max + plot_x_margin)
)
self.error_plot.add_plot(
lambda axes: axes.plot(
x_values,
np.abs(y_values - y_interpolated),
color="blue",
label="|f(x) - L(x)|",
)
)
self.function_plot.redraw()
self.error_plot.redraw()
def parse_function(self, func_str: str) -> Callable[[float], float]:
func = sympy.sympify(func_str)
params = []
for name in func.atoms(sympy.Symbol):
params.append(str(name))
if len(params) == 0 or params.count("x") < 1:
raise ValueError("No x in function")
func_lambda = sympy.lambdify(params, func, cse=True)
if func_lambda.__code__.co_argcount != len(params):
raise ValueError("Bad arguments count")
params = [p for p in params if p != "x"]
old_params = self.function_params
if set(old_params.keys()) != set(params):
self.recreate_params_field(params)
def f(x: float) -> float:
return func_lambda(x=x, **self.function_params)
return f
def update_function(self):
if self.parsing_function:
return
try:
self.recalculate_interpolated_function()
self.redraw_plots()
except Exception as e:
print(e)
def recalculate_interpolated_function(self):
points = [self.x_0, self.x_n]
points[1:1] = self.points
points = np.array(points)
self.interpolated_function = algorithm.make_forward_interpolate_function(
self.function, points
)
# self.interpolated_function = algorithm.make_backward_interpolate_function(
# self.function, points
# )
def recreate_params_field(self, params: List[str]):
self.function_param_fields.recreate(params)
def recreate_points_field(self):
points = np.linspace(self.x_0, self.x_n, self.n + 1)
points = [float(p) for p in points[1:-1]]
self.points_field.recreate(
1,
points,
self.x_0 + 1 / self.points_field.DIVISIONS,
self.x_n - 1 / self.points_field.DIVISIONS,
)
self.points = points
def _function_field_changed(self, w: widgets.InputWidget) -> bool:
try:
self.parsing_function = True
self.function = self.parse_function(w.get_value())
self.parsing_function = False
except Exception as e:
print(f"{e}")
self.parsing_function = False
return False
self.update_function()
return True
def _function_param_field_changed(self, w: widgets.InputWidget) -> bool:
self.function_params = self.function_param_fields.get_value()
self.update_function()
return True
def _x_0_field_changed(self, w: widgets.InputWidget) -> bool:
value = float(w.get_value())
if value == self.x_n:
w.value = w.previous_value
return False
self.x_0 = value
self.recreate_points_field()
self.update_function()
return True
def _x_n_field_changed(self, w: widgets.InputWidget) -> bool:
value = float(w.get_value())
if value == self.x_0:
w.value = w.previous_value
return False
self.x_n = value
self.recreate_points_field()
self.update_function()
return True
def _n_slider_changed(self, w: widgets.InputWidget) -> bool:
self.n = int(w.get_value())
self.n_display.set_text(str(self.n))
self.recreate_points_field()
# self.update_function()
return True
def _points_field_changed(self, w: widgets.InputWidget) -> bool:
self.points = w.get_value()
self.update_function()
return True
def _margin_slider_changed(self, w: widgets.InputWidget) -> bool:
self.margin = (float(w.get_value()) - 250) / 250.0
self.margin_display.set_text(f"{self.margin * 100:.2f}%")
self.redraw_plots()
return True

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Л5-В6/Lab_5.pdf Normal file
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Л5-В6/Блоксхема.drawio Normal file
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2
Л5-В6/Программа/.gitignore vendored Normal file
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.venv
*/__pycache__

5
Л5-В6/Программа/requirements.txt Normal file
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sympy
numpy
scipy
pyqt6
matplotlib

45
Л5-В6/Программа/src/algorithm.py Normal file
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import numpy as np
import typing
def runge_kutta_4(
x_0: float,
y_0: typing.List[float],
x_n: float,
h: float,
f: typing.List[typing.Callable[[float, typing.List[float]], float]],
) -> typing.Dict[float, np.ndarray]:
count = len(y_0)
if count != len(f):
raise ValueError("len(y_0) != len(f)")
x_i = x_0
y_i = np.array(y_0, dtype=np.float64)
result = {x_i: y_i}
while x_i < x_n + h / 2:
y_i = calculate_y(x_i, y_i, h, f)
x_i += h
result[x_i] = y_i
return result
def calculate_y(x_i, y_i, h, f):
k_1 = np.array([f[i](x_i, y_i) for i in range(len(y_i))], dtype=np.float64)
k_2 = np.array(
[f[i](x_i + h / 2, y_i + h * k_1 / 2) for i in range(len(y_i))],
dtype=np.float64,
)
k_3 = np.array(
[f[i](x_i + h / 2, y_i + h * k_2 / 2) for i in range(len(y_i))],
dtype=np.float64,
)
k_4 = np.array(
[f[i](x_i + h, y_i + h * k_3) for i in range(len(y_i))], dtype=np.float64
)
y_i = y_i + h / 6 * (k_1 + 2 * k_2 + 2 * k_3 + k_4)
return y_i

17
Л5-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
import widgets
if __name__ == "__main__":
widgets.setup_dark_theme()
app = QApplication(sys.argv)
font = QFont("Cascadia Code", 14)
app.setFont(font)
window = window.MainWindow()
window.show()
sys.exit(app.exec())

68
Л5-В6/Программа/src/task.py Normal file
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import sympy
import typing
f_str = "y * ln(y) / sin(x)"
f_expr = sympy.sympify(f_str)
f_l = sympy.lambdify("x, y", f_expr, cse=True)
def task1_f(x: float, y: typing.List[float]) -> float:
return f_l(x, *y)
def task1_f_display() -> str:
return f_str
f_1_str = "sin(x**2 + y_2**2)"
f_1_expr = sympy.sympify(f_1_str)
f_1_l = sympy.lambdify("x, y_1, y_2", f_1_expr, cse=True)
f_2_str = "cos(x * y_1)"
f_2_expr = sympy.sympify(f_2_str)
f_2_l = sympy.lambdify("x, y_1, y_2", f_2_expr, cse=True)
def task2_f_1(x: float, y: typing.List[float]) -> float:
return f_1_l(x, *y)
def task2_f_2(x: float, y: typing.List[float]) -> float:
return f_2_l(x, *y)
def task2_f_1_display() -> str:
return f_1_str
def task2_f_2_display() -> str:
return f_2_str
def task3_f_display() -> str:
return "y'' + a1 * y' + a2 * y"
x, a1, a2 = sympy.symbols("x a1 a2", real=True)
y = sympy.symbols("y", cls=sympy.Function)(x)
yp = y.diff(x)
ypp = y.diff(x, 2)
f_xy = ypp + a1 * yp + a2 * y
task3_generic_solution = sympy.dsolve(f_xy, y).rhs
def task3_solution_display() -> str:
return str(task3_generic_solution)
def task3_make_f_sympy(a1_, a2_, x_0_, y_0_, y_d_0_):
solution = task3_generic_solution.subs({a1: a1_, a2: a2_})
cnd1 = sympy.Eq(solution.subs(x, x_0_), y_0_)
cnd2 = sympy.Eq(solution.diff(x).subs(x, x_0_), y_d_0_)
C1, C2 = sympy.symbols("C1 C2")
C1C2_sl = sympy.solve([cnd1, cnd2], (C1, C2))
return sympy.simplify(solution.subs(C1C2_sl))

330
Л5-В6/Программа/src/widgets.py Normal file
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from io import BytesIO
from PyQt6.QtWidgets import (
QLabel,
QWidget,
QLineEdit,
QHBoxLayout,
QSlider,
QVBoxLayout,
)
from PyQt6.QtCore import Qt
from PyQt6.QtSvgWidgets import QSvgWidget
import matplotlib
import matplotlib.figure
import matplotlib.axes
from matplotlib.backends.backend_qtagg import (
FigureCanvasQTAgg as FigureCanvas,
NavigationToolbar2QT as NavigationToolbar,
)
import sympy
import abc
import typing
import matplotlib.pyplot
def setup_dark_theme():
matplotlib.pyplot.style.use(
{
"figure.facecolor": "#1e1e1e",
"savefig.facecolor": "#1e1e1e",
"text.color": "white",
"xtick.color": "white",
"ytick.color": "white",
"legend.facecolor": "#1e1e1e",
"legend.edgecolor": "white",
"legend.labelcolor": "white",
"grid.color": "white",
"figure.edgecolor": "white",
"axes.facecolor": "#1e1e1e",
"axes.axisbelow": "true",
"axes.edgecolor": "white",
"axes.labelcolor": "white",
"axes.grid": True,
"axes.spines.left": False,
"axes.spines.right": False,
"axes.spines.top": False,
"axes.spines.bottom": False,
}
)
class DisplayField(QWidget):
label: str
def __init__(self, parent, label="", text="", wrap=False):
super().__init__(parent)
self._layout = QHBoxLayout(self)
self._layout.setContentsMargins(0, 0, 0, 0)
self.label = label
self.text = QLabel(f"{self.label}{text}")
self.text.setWordWrap(wrap)
self.text.setAlignment(Qt.AlignmentFlag.AlignLeft)
self._layout.addWidget(self.text)
def set_visible(self, visible):
self.text.setVisible(visible)
def set_text(self, text):
self.text.setText(f"{self.label}{text}")
class InputWidget(QWidget):
value: typing.Any
previous_value: typing.Any
callback: typing.Callable[[typing.Self], bool] | None = None
def init(self):
self.value = self._get_value_internal()
self.previous_value = self.value
self._set_callback_internal(self._on_change_internal)
def get_value(self) -> typing.Any:
return self.value
def get_previous_value(self) -> typing.Any:
return self.previous_value
def set_value(self, value: typing.Any):
self._set_value_internal(value)
self._set_value_no_sync(value)
def set_callback(self, callback: typing.Callable[[typing.Self], bool]):
self.callback = callback
@abc.abstractmethod
def _get_value_internal(self) -> typing.Any:
pass
@abc.abstractmethod
def _set_value_internal(self, value: typing.Any):
pass
@abc.abstractmethod
def _set_callback_internal(self, callback: typing.Callable[[], None]):
pass
def _set_value_no_sync(self, value: typing.Any):
self.previous_value = self.value
self.value = value
def _on_change_internal(self):
self._set_value_no_sync(self._get_value_internal())
if self.callback:
self.callback(self)
def make_callback_chain(
callbacks: typing.List[typing.Callable[[InputWidget], bool]]
) -> typing.Callable[[InputWidget], bool]:
def callback(widget: InputWidget):
for callback in callbacks:
if not callback(widget):
break
return True
return callback
def make_min_max_callback(
min: typing.Any, max: typing.Any
) -> typing.Callable[[InputWidget], bool]:
def callback(widget: InputWidget):
value = widget.get_value()
if type(min)(value) < min:
widget.set_value(min)
if type(max)(value) > max:
widget.set_value(max)
return True
return callback
def float_check_callback(widget: InputWidget):
try:
internal_value = widget._get_value_internal()
if not (internal_value == "" or internal_value == "-" or internal_value == "."):
_ = float(widget.get_value())
return True
else:
widget.value = widget.previous_value
return False
except:
widget.set_value(widget.previous_value)
return False
def int_check_callback(widget: InputWidget):
try:
internal_value = widget._get_value_internal()
if not (internal_value == "" or internal_value == "-"):
_ = int(widget.get_value())
return True
else:
widget.value = widget.previous_value
return False
except:
widget.set_value(widget.previous_value)
return False
class InputField(InputWidget):
def __init__(
self,
parent,
label_text="",
placeholder_text="",
lineedit_text="",
label_position="left",
):
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.lineedit.setMinimumWidth(50)
if label_position == "left":
self._layout.addWidget(self.label)
self._layout.addWidget(self.lineedit)
elif label_position == "right":
self._layout.addWidget(self.lineedit)
self._layout.addWidget(self.label)
elif label_position == "none":
self._layout.addWidget(self.lineedit)
super().init()
super().set_value(lineedit_text)
def _get_value_internal(self):
return self.lineedit.text()
def _set_value_internal(self, value):
self.lineedit.setText(str(value))
def _set_callback_internal(self, callback):
self.lineedit.textChanged.connect(callback)
class MathInputField(InputField):
internal_value: typing.Any
def __init__(
self,
parent,
label_text="",
placeholder_text="",
lineedit_value="0.0",
label_position="left",
):
super().__init__(
parent, label_text, placeholder_text, lineedit_value, label_position
)
def _get_value_internal(self):
try:
self.internal_value = str(
float(
sympy.sympify(self.lineedit.text()).evalf(
subs={
"e": sympy.E,
"Pi": sympy.pi,
"PI": sympy.pi,
}
)
)
)
except:
pass
return self.internal_value
class InputSlider(InputWidget):
slider: QSlider
def __init__(
self,
parent,
label_text="",
value=0,
min_value=0,
max_value=100,
step=1,
ticks=False,
):
super().__init__(parent)
self._layout = QHBoxLayout(self)
self._layout.setContentsMargins(0, 0, 0, 0)
self.label = QLabel(label_text)
self.slider = QSlider(Qt.Orientation.Horizontal)
if ticks:
self.slider.setTickPosition(QSlider.TickPosition.TicksBelow)
self.slider.setTickInterval(step)
self.slider.setMinimum(min_value)
self.slider.setMaximum(max_value)
self.slider.setValue(value)
self.slider.setSingleStep(step)
self._layout.addWidget(self.label)
self._layout.addWidget(self.slider)
super().init()
super().set_value(value)
def _get_value_internal(self):
return self.slider.value()
def _set_value_internal(self, value):
self.slider.setValue(value)
def _set_callback_internal(self, callback):
self.slider.valueChanged.connect(callback)
class PlotWidget(QWidget):
figure: matplotlib.figure.Figure
toolbar: NavigationToolbar = None
canvas: FigureCanvas
def __init__(self, parent, figure: matplotlib.figure.Figure, toolbar: bool = False):
super().__init__(parent)
self._layout = QVBoxLayout(self)
self.figure = figure
self.canvas = FigureCanvas(self.figure)
self.canvas.setStyleSheet("background-color:transparent;")
if toolbar:
self.toolbar = NavigationToolbar(self.canvas, self)
self._layout.addWidget(self.toolbar)
self._layout.addWidget(self.canvas)
def set_figure(self, figure: matplotlib.figure.Figure):
self.figure = figure
self.canvas = FigureCanvas(self.figure)
self._layout.addWidget(self.canvas)
self.redraw()
def get_figure(self) -> matplotlib.figure.Figure:
return self.figure
def redraw(self):
self.canvas.draw()

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Л5-В6/Программа/src/window.py Normal file
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from PyQt6.QtWidgets import (
QMainWindow,
QLabel,
QPushButton,
QFormLayout,
QWidget,
QHBoxLayout,
QTabWidget,
)
from PyQt6 import QtWidgets
import matplotlib
import matplotlib.pyplot as plt
matplotlib.use("QtAgg")
import numpy as np
import sympy
import typing
import widgets
import task
import algorithm
class MainWindow(QMainWindow):
def __init__(self):
super().__init__()
self.setup_ui()
def setup_ui(self):
self.setWindowTitle("Лабораторная работа №5")
self.setFixedSize(800, 900)
central_widget = QTabWidget(self)
central_widget.setTabsClosable(False)
central_widget.setContentsMargins(0, 0, 0, 0)
central_widget.addTab(Tab1(central_widget), "Задание 1")
central_widget.addTab(Tab2(central_widget), "Задание 2")
central_widget.addTab(Tab3(central_widget), "Задание 3")
self.setCentralWidget(central_widget)
class Tab1(QWidget):
initialized = False
x_0_field: widgets.InputField
y_0_field: widgets.InputField
x_n_field: widgets.InputField
h_display: widgets.DisplayField
h_field: widgets.InputSlider
x_0: float
y_0: float
x_n: float
h: float
solution_plot: widgets.PlotWidget
solution_figure: plt.Figure
solution_axes: plt.Axes
def __init__(self, parent):
super().__init__(parent)
self._initialize()
self.reset()
self.initialized = True
self.update_solution()
def _initialize(self):
self._layout = QFormLayout(self)
self._function_display = widgets.DisplayField(self, "f(x, y) = ", "")
self._layout.addWidget(self._function_display)
self.x_0_field = widgets.MathInputField(self, label_text="x_0: ")
self.x_0_field.set_callback(
widgets.make_callback_chain(
[widgets.float_check_callback, self._x_0_field_changed]
)
)
self._layout.addWidget(self.x_0_field)
self.y_0_field = widgets.MathInputField(self, label_text="y_0: ")
self.y_0_field.set_callback(
widgets.make_callback_chain(
[widgets.float_check_callback, self._y_0_field_changed]
)
)
self._layout.addWidget(self.y_0_field)
self.x_n_field = widgets.MathInputField(self, label_text="x_n: ")
self.x_n_field.set_callback(
widgets.make_callback_chain(
[widgets.float_check_callback, self._x_n_field_changed]
)
)
self._layout.addWidget(self.x_n_field)
self.h_display = widgets.DisplayField(self, "h: ", "")
self._layout.addWidget(self.h_display)
self.h_field = widgets.InputSlider(
self, label_text="", value=0, min_value=1, max_value=100, step=1
)
self.h_field.set_callback(self._h_field_changed)
self._layout.addWidget(self.h_field)
self.solution_figure = plt.figure()
self.solution_figure.patch.set_facecolor("none")
self.solution_axes = self.solution_figure.add_subplot(111)
self.solution_figure.tight_layout(pad=3.0)
self.solution_plot = widgets.PlotWidget(self, self.solution_figure, True)
self._layout.addWidget(self.solution_plot)
def reset(self):
self._function_display.set_text(task.task1_f_display())
self.x_0_field.set_value("pi / 2")
self.y_0_field.set_value("e")
self.x_n_field.set_value("pi")
self.h_field.set_value(5)
QtWidgets.QApplication.processEvents()
def _x_0_field_changed(self, w: widgets.InputWidget) -> bool:
self.x_0 = float(w.get_value())
self.update_solution()
return True
def _y_0_field_changed(self, w: widgets.InputWidget) -> bool:
self.y_0 = float(w.get_value())
return True
def _x_n_field_changed(self, w: widgets.InputWidget) -> bool:
self.x_n = float(w.get_value())
self.update_solution()
return True
def _h_field_changed(self, w: widgets.InputWidget) -> bool:
self.h = float(w.get_value()) / 100.0
self.h_display.set_text(str(self.h))
self.update_solution()
return True
def update_solution(self):
if not self.initialized:
return
solution = algorithm.runge_kutta_4(
self.x_0, [self.y_0], self.x_n, self.h, [task.task1_f]
)
x = np.array(list(solution.keys()))
y = np.array(list(map(lambda x: x[0], solution.values())))
self.solution_axes.clear()
self.solution_axes.set_xlabel("x")
self.solution_axes.set_ylabel("y")
self.solution_axes.grid(True)
self.solution_axes.plot(x, y, label="y(x)")
solution = algorithm.runge_kutta_4(
self.x_0, [self.y_0], self.x_n, self.h / 2, [task.task1_f]
)
x = np.array(list(solution.keys()))
y = np.array(list(map(lambda x: x[0], solution.values())))
self.solution_axes.plot(x, y, label="y(x) (h/2)")
solution = algorithm.runge_kutta_4(
self.x_0, [self.y_0], self.x_n, self.h * 2, [task.task1_f]
)
x = np.array(list(solution.keys()))
y = np.array(list(map(lambda x: x[0], solution.values())))
self.solution_axes.plot(x, y, label="y(x) (h*2)")
self.solution_axes.set_yscale("log")
self.solution_axes.legend(loc="upper left")
self.solution_plot.redraw()
class Tab2(QWidget):
initialized = False
_function1_display: widgets.DisplayField
_function2_display: widgets.DisplayField
x_0_field: widgets.InputField
y_10_field: widgets.InputField
y_20_field: widgets.InputField
x_n_field: widgets.InputField
h_display: widgets.DisplayField
h_field: widgets.InputSlider
x_0: float
y_10: float
y_20: float
x_n: float
h: float
def __init__(self, parent):
super().__init__(parent)
self._initialize()
self.reset()
self.initialized = True
self.update_solution()
def _initialize(self):
self._layout = QFormLayout(self)
self._function1_display = widgets.DisplayField(self, "f1(x, y) = ", "")
self._layout.addWidget(self._function1_display)
self._function2_display = widgets.DisplayField(self, "f2(x, y) = ", "")
self._layout.addWidget(self._function2_display)
self.x_0_field = widgets.MathInputField(self, label_text="x_0: ")
self.x_0_field.set_callback(
widgets.make_callback_chain(
[widgets.float_check_callback, self._x_0_field_changed]
)
)
self._layout.addWidget(self.x_0_field)
self.y_10_field = widgets.MathInputField(self, label_text="y_10: ")
self.y_10_field.set_callback(
widgets.make_callback_chain(
[widgets.float_check_callback, self._y_10_field_changed]
)
)
self._layout.addWidget(self.y_10_field)
self.y_20_field = widgets.MathInputField(self, label_text="y_20: ")
self.y_20_field.set_callback(
widgets.make_callback_chain(
[widgets.float_check_callback, self._y_20_field_changed]
)
)
self._layout.addWidget(self.y_20_field)
self.x_n_field = widgets.MathInputField(self, label_text="x_n: ")
self.x_n_field.set_callback(
widgets.make_callback_chain(
[widgets.float_check_callback, self._x_n_field_changed]
)
)
self._layout.addWidget(self.x_n_field)
self.h_display = widgets.DisplayField(self, "h: ", "")
self._layout.addWidget(self.h_display)
self.h_field = widgets.InputSlider(
self, label_text="", value=0, min_value=1, max_value=100, step=1
)
self.h_field.set_callback(self._h_field_changed)
self._layout.addWidget(self.h_field)
self.solution_figure = plt.figure()
self.solution_figure.patch.set_facecolor("none")
self.solution_axes = self.solution_figure.add_subplot(111)
self.solution_figure.tight_layout(pad=3.0)
self.solution_plot = widgets.PlotWidget(self, self.solution_figure)
self._layout.addWidget(self.solution_plot)
def reset(self):
self._function1_display.set_text(task.task2_f_1_display())
self._function2_display.set_text(task.task2_f_2_display())
self.x_0_field.set_value("0")
self.y_10_field.set_value("0")
self.y_20_field.set_value("0")
self.x_n_field.set_value("4")
self.h_field.set_value(5)
QtWidgets.QApplication.processEvents()
def _x_0_field_changed(self, w: widgets.InputWidget) -> bool:
self.x_0 = float(w.get_value())
self.update_solution()
return True
def _y_10_field_changed(self, w: widgets.InputWidget) -> bool:
self.y_10 = float(w.get_value())
self.update_solution()
return True
def _y_20_field_changed(self, w: widgets.InputWidget) -> bool:
self.y_20 = float(w.get_value())
self.update_solution()
return True
def _x_n_field_changed(self, w: widgets.InputWidget) -> bool:
self.x_n = float(w.get_value())
self.update_solution()
return True
def _h_field_changed(self, w: widgets.InputWidget) -> bool:
self.h = float(w.get_value()) / 100.0
self.h_display.set_text(str(self.h))
self.update_solution()
return True
def update_solution(self):
if not self.initialized:
return
solution = algorithm.runge_kutta_4(
self.x_0,
[self.y_10, self.y_20],
self.x_n,
self.h,
[task.task2_f_1, task.task2_f_2],
)
x = np.array(list(solution.keys()))
y1 = np.array(list(map(lambda x: x[0], solution.values())))
y2 = np.array(list(map(lambda x: x[1], solution.values())))
self.solution_axes.cla()
self.solution_axes.plot(x, y1, label="y_1")
self.solution_axes.plot(x, y2, label="y_2")
self.solution_axes.legend()
self.solution_plot.redraw()
class Tab3(QWidget):
initialized = False
a1_field: widgets.InputField
a2_field: widgets.InputField
x_0_field: widgets.InputField
y_0_field: widgets.InputField
y_d_0_field: widgets.InputField
generic_solution_display: widgets.DisplayField
solution_display: widgets.DisplayField
a1: float
a2: float
x_0: float
y_0: float
y_d_0: float
solution_plot: widgets.PlotWidget
solution_figure: plt.Figure
solution_axes: plt.Axes
def __init__(self, parent):
super().__init__(parent)
self._initialize()
self.reset()
self.initialized = True
self.update_solution()
def _initialize(self):
self._layout = QFormLayout(self)
self._function_display = widgets.DisplayField(
self, task.task3_f_display(), " = 0"
)
self._layout.addWidget(self._function_display)
self.a1_field = widgets.InputField(
self,
"a1: ",
)
self.a1_field.set_callback(
widgets.make_callback_chain(
[widgets.float_check_callback, self._a1_changed]
)
)
self._layout.addWidget(self.a1_field)
self.a2_field = widgets.InputField(
self,
"a2: ",
)
self.a2_field.set_callback(
widgets.make_callback_chain(
[widgets.float_check_callback, self._a2_changed]
)
)
self._layout.addWidget(self.a2_field)
self.x_0_field = widgets.InputField(
self,
"x_0: ",
)
self.x_0_field.set_callback(
widgets.make_callback_chain(
[widgets.float_check_callback, self._x_0_field_changed]
)
)
self._layout.addWidget(self.x_0_field)
self.y_0_field = widgets.InputField(
self,
"y_0: ",
)
self.y_0_field.set_callback(
widgets.make_callback_chain(
[widgets.float_check_callback, self._y_0_field_changed]
)
)
self._layout.addWidget(self.y_0_field)
self.y_d_0_field = widgets.InputField(
self,
"y_d_0: ",
)
self.y_d_0_field.set_callback(
widgets.make_callback_chain(
[widgets.float_check_callback, self._y_d_0_field_changed]
)
)
self._layout.addWidget(self.y_d_0_field)
self.generic_solution_display = widgets.DisplayField(
self, "Общее решение: ", wrap=True
)
self._layout.addWidget(self.generic_solution_display)
self.solution_display = widgets.DisplayField(self, "Решение: ", wrap=True)
self._layout.addWidget(self.solution_display)
self.solution_figure = plt.figure()
self.solution_figure.patch.set_facecolor("none")
self.solution_axes = self.solution_figure.add_subplot(111)
self.solution_figure.tight_layout(pad=3.0)
self.solution_plot = widgets.PlotWidget(self, self.solution_figure, True)
self._layout.addWidget(self.solution_plot)
def reset(self):
self.a1_field.set_value("-4.0")
self.a2_field.set_value("4.0")
self.x_0_field.set_value("0.3")
self.y_0_field.set_value("1.0")
self.y_d_0_field.set_value("1.0")
QtWidgets.QApplication.processEvents()
def _a1_changed(self, w: widgets.InputWidget) -> bool:
self.a1 = float(w.get_value())
self.update_solution()
return True
def _a2_changed(self, w: widgets.InputWidget) -> bool:
self.a2 = float(w.get_value())
self.update_solution()
return True
def _x_0_field_changed(self, w: widgets.InputWidget) -> bool:
self.x_0 = float(w.get_value())
self.update_solution()
return True
def _y_0_field_changed(self, w: widgets.InputWidget) -> bool:
self.y_0 = float(w.get_value())
self.update_solution()
return True
def _y_d_0_field_changed(self, w: widgets.InputWidget) -> bool:
self.y_d_0 = float(w.get_value())
self.update_solution()
return True
def update_solution(self):
if not self.initialized:
return
self.generic_solution_display.set_text(
"\n" + str(task.task3_solution_display())
)
solution = task.task3_make_f_sympy(
self.a1, self.a2, self.x_0, self.y_0, self.y_d_0
)
self.solution_display.set_text(str(solution))
try:
f = sympy.lambdify("x", solution, cse=True)
x = np.linspace(self.x_0, self.x_0 + 5, 100)
y = f(x)
self.solution_axes.clear()
self.solution_axes.grid(True)
self.solution_axes.plot(x, y, label="y")
self.solution_axes.legend()
self.solution_plot.redraw()
except Exception as e:
print(e)