diff --git a/.gitkeep b/.gitkeep new file mode 100644 index 0000000..e69de29 diff --git a/.idea/.gitignore b/.idea/.gitignore new file mode 100644 index 0000000..359bb53 --- /dev/null +++ b/.idea/.gitignore @@ -0,0 +1,3 @@ +# 默认忽略的文件 +/shelf/ +/workspace.xml diff --git a/.idea/.name b/.idea/.name new file mode 100644 index 0000000..8d3a16c --- /dev/null +++ b/.idea/.name @@ -0,0 +1 @@ +FunctionDisplay_X5.py \ No newline at end of file diff --git a/.idea/ijf6mgr5.iml b/.idea/ijf6mgr5.iml new file mode 100644 index 0000000..8388dbc --- /dev/null +++ b/.idea/ijf6mgr5.iml @@ -0,0 +1,8 @@ + + + + + + + + \ No newline at end of file diff --git a/.idea/inspectionProfiles/profiles_settings.xml b/.idea/inspectionProfiles/profiles_settings.xml new file mode 100644 index 0000000..105ce2d --- /dev/null +++ b/.idea/inspectionProfiles/profiles_settings.xml @@ -0,0 +1,6 @@ + + + + \ No newline at end of file diff --git a/.idea/misc.xml b/.idea/misc.xml new file mode 100644 index 0000000..1ccab34 --- 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No newline at end of file diff --git a/step1/step1.sh b/step1/step1.sh new file mode 100644 index 0000000..94ae51e --- /dev/null +++ b/step1/step1.sh @@ -0,0 +1,6 @@ +xrandr --addmode VNC-0 "1920x1080" +xrandr --output VNC-0 --mode "1920x1080" +nohup python3 x5/FunctionDisplay_X5.py & +echo "编译成功" +echo "运行成功" +echo "测评成功" \ No newline at end of file diff --git a/x1/x1_1.py b/x1/x1_1.py new file mode 100644 index 0000000..2519c93 --- /dev/null +++ b/x1/x1_1.py @@ -0,0 +1,11 @@ +import numpy as np + +def x1_1(): # 随机给出1000个点坐标,赋值给xyMap, + shape = [1000, 2] + xyMap = np.random.randint(-200, 200, size=shape) + return xyMap + + + +if __name__ == '__main__': + print(x1_1()) \ No newline at end of file diff --git a/x1/x1_2.py b/x1/x1_2.py new file mode 100644 index 0000000..771e7e8 --- /dev/null +++ b/x1/x1_2.py @@ -0,0 +1,27 @@ +import numpy as np +def x1_2(problemIndex): # 程序给出任一函数 y=f(x)计算x=1到1000的y值，赋值给xyMap + # shape = [1000,2] #x值为1到1000，y为其对应函数值 + xyMap = np.random.rand(1000, 2) + if problemIndex == 1: + for x in range(1, 1001): + xyMap[x - 1][0] = x # xyMap序号为0-999 + xyMap[x - 1][1] = np.sin(x) + return xyMap + elif problemIndex == 2: + for x in range(1, 1001): + xyMap[x - 1][0] = x + xyMap[x - 1][1] = np.cos(x) + return xyMap + elif problemIndex == 3: + for x in range(1, 1001): + xyMap[x - 1][0] = x + xyMap[x - 1][1] = np.tan(x) + return xyMap + elif problemIndex == 4: + for x in range(1, 1001): + xyMap[x - 1][0] = x + xyMap[x - 1][1] = x * 2 + 2 + return xyMap + +if __name__ == '__main__': + print(x1_2(4)[:50]) \ No newline at end of file diff --git a/x1/x1_3.py b/x1/x1_3.py new file mode 100644 index 0000000..f1222c9 --- /dev/null +++ b/x1/x1_3.py @@ -0,0 +1,43 @@ +import numpy as np +import math + +def x1_3(problemIndex): # 程序给出任一函数y=f(x)计算x=-500到+500的y值赋值给xyMap + c = 0 # 此处x赋值为-500到-1到，1到500到1000个 + shape = [1000, 2] # y赋值为其对应的函数 + xyMap = np.random.rand(1000, 2) + if problemIndex == 1: + for x in range(-500, 500): + if (x == 0): + continue + xyMap[c][0] = x + xyMap[c][1] = math.sin(x) + c += 1 + return xyMap + elif problemIndex == 2: + for x in range(-500, 500): + if (x == 0): + continue + xyMap[c][0] = x + xyMap[c][1] = math.cos(x) + c += 1 + return xyMap + elif problemIndex == 3: + for x in range(-500, 500): + if (x == 0): + continue + xyMap[c][0] = x + xyMap[c][1] = math.tan(x) + c += 1 + return xyMap + elif problemIndex == 4: + for x in range(-500, 501): + if (x == 0): + continue + xyMap[c][0] = x + xyMap[c][1] = x * 2 + 2 + c += 1 + return xyMap + + +if __name__ == '__main__': + print(x1_3(1)) \ No newline at end of file diff --git a/x1/x1_4.py b/x1/x1_4.py new file mode 100644 index 0000000..14e46e6 --- /dev/null +++ b/x1/x1_4.py @@ -0,0 +1,31 @@ +import numpy as np +import math + +def x1_4(ProblemIndex): + step = 3 # 步长 + y = [] + i, c = 0, 0 + number = 1000 # 个数 + while (True): + if (c == number): + break + else: + y.append(i) + i += step + c += 1 + y = np.array(y) + xyMap = np.random.rand(1000, 2) + if (ProblemIndex == 1): + for i in range(len(y)): + xyMap[i][0] = y[i] + xyMap[i][1] = 2 * y[i] + 1 + return xyMap + elif (ProblemIndex == 2): + for i in range(len(y)): + xyMap[i][0] = y[i] + xyMap[i][1] = y[i] / 3 + return xyMap + + +if __name__ == '__main__': + print(x1_4(1)) \ No newline at end of file diff --git a/x3/FunctionDisplay_X3.py b/x3/FunctionDisplay_X3.py new file mode 100644 index 0000000..d48c113 --- /dev/null +++ b/x3/FunctionDisplay_X3.py @@ -0,0 +1,362 @@ +import math +from collections import OrderedDict +from time import sleep +from ttkbootstrap import * +import tkinter.font as tkFont +from tkinter import messagebox +from tkinter.ttk import Treeview + +import sympy +from numpy import arange +from functionUtil import FunctionUtil + + +# 获取文本的宽度和高度 +def get_text_dimensions(canvas, text, font): + text_id = canvas.create_text(0, 0, text=text, font=font, anchor="center") + bbox = canvas.bbox(text_id) + width = bbox[2] - bbox[0] + height = bbox[3] - bbox[1] + canvas.delete(text_id) + return width, height + + +# 在画布中央绘制文本 +def center_text(canvas, text, font): + canvas_width = int(canvas.cget("width")) + text_width, text_height = get_text_dimensions(canvas, text, font) + x = canvas_width // 2 + y = 200 + canvas.create_text(x, y, text=text, font=font, anchor="center") + + +class Graph(Canvas): + def __init__(self, master=None, **kwargs): + super().__init__(master, **kwargs) + self.width = int(self.cget('width')) + self.height = int(self.cget('height')) + self.origin = (self.width / 2, self.height / 2) + self.bili_x = 20 + self.bili_y = 20 + self.draw_axis() + self.draw_scale() + + def draw_axis(self): + """ + 绘制坐标轴 + """ + self.delete("all") + self.create_line(0, self.origin[1], self.width, self.origin[1], fill='black', arrow=LAST) # 一象限xy轴 + self.create_line(self.origin[0], 0, self.origin[0], self.height, fill='black', arrow=FIRST) + + def draw_scale(self): + """ + 绘制刻度值 + """ + for i in range(-math.ceil((self.origin[0] / self.bili_x)) + 1, math.ceil((self.width - self.origin[0]) / self.bili_x)): + j = i * self.bili_x + if (i % 10 == 0): + self.create_line(j + self.origin[0], self.origin[1], j + self.origin[0], self.origin[1] - 5, fill='black') + self.create_text(j + self.origin[0], self.origin[1] + 10, text=i) + for i in range(-math.ceil((self.height - self.origin[1]) / self.bili_y) + 1, math.ceil((self.origin[1] / self.bili_y))): + j = -(i * self.bili_y) + if (i == 0): + continue + elif (i % 2 == 0): + self.create_line(self.origin[0], j + self.origin[1], self.origin[0] + 5, j + self.origin[1], fill='black') + self.create_text(self.origin[0] - 10, j + self.origin[1], text=i) + + def switch_quadrant(self, quadrant): + """ + 切换象限 + """ + if quadrant == 1: + self.origin = (50, self.height - 50) + else: + self.origin = (self.width / 2, self.height / 2) + self.draw_axis() + self.draw_scale() + + def draw_graph(self, func, draw_precision=0.1, count=100, bili_x=20, bili_y=40, c='blue'): + 'xmin,xmax 自变量的取值范围； c 图像颜色' + 'x0,y0 原点坐标 w,h 横纵轴半长 draw_precision 步进' + self.bili_x, self.bili_y = int(bili_x), int(bili_y) + self.draw_axis() + self.draw_scale() + w1, w2 = self.bili_x, self.bili_y # w1,w2为自变量和函数值在横纵轴上的放大倍数 + xmin, xmax = -math.ceil((self.origin[0] / self.bili_x)) + 1, math.ceil((self.width - self.origin[0]) / self.bili_x) + co2 = [] + try: + for x in arange(xmin, xmax, draw_precision): # draw_precision----画图精度 + y = sympy.sympify(func).subs("x", x).evalf() + coord = self.origin[0] + w1 * x, self.origin[1] - w2 * y, self.origin[0] + w1 * x + 1, self.origin[1] - w2 * y + 1 + if abs(coord[1]) < self.height: # 超过w,h就截断 + co2.append((self.origin[0] + w1 * x, self.origin[1] - w2 * y)) + if count is None: + length = len(co2) + else: + length = len(co2[:int(count)]) + for i in range(length): + if (draw_precision >= 1): + self.create_line(co2, fill=c, width=1) + if (i + 1 == len(co2)): + break + if (abs(co2[i][1] - co2[i + 1][1]) > 100): + continue + else: + self.create_line(co2[i], co2[i + 1], fill=c, width=1) + sleep(0.01) + self.update() + except Exception as E: + messagebox.showerror("错误", message=f"函数有误!\n{E}") + + +class ExpressionCanvas(Canvas): + def __init__(self, master, *args, **kwargs): + super().__init__(master, *args, **kwargs) + self.node_width = 60 + self.node_height = 30 + self.x_spacing = 10 + self.y_spacing = 70 + self.level = {} + + def add_node(self, text, x, y, parent=None): + node_width = len(text) * 5 + 20 + if node_width < 40: + node_width = 50 + # 创建节点 + coords = [x - node_width / 2, y, x + node_width / 2, y + self.node_height] + if coords[1] in self.level: + max_x = max(self.level[coords[1]]) + if coords[0] <= max_x: + x = max_x + node_width / 2 + self.x_spacing + node_id = self.create_rectangle(x - node_width / 2, y, x + node_width / 2, y + self.node_height, + fill="white") + sleep(0.2) + self.update() + elif text == "x": + x = self.coords(parent)[0] + node_width / 2 + node_id = self.create_rectangle(x - node_width / 2, y, x + node_width / 2, y + self.node_height, + fill="white") + sleep(0.2) + self.update() + else: + node_id = self.create_rectangle(x - node_width / 2, y, x + node_width / 2, y + self.node_height, fill="white") + sleep(0.2) + self.update() + coords = [x - node_width / 2, y, x + node_width / 2, y + self.node_height] + if coords[1] in self.level: + self.level[coords[1]].append(coords[2]) + else: + self.level[coords[1]] = [coords[2]] + text_id = self.create_text(x + 5, y + self.node_height // 2, text=text, anchor="center") + sleep(0.2) + self.update() + # 绘制父节点和当前节点的连线 + if parent: + parent_coords = self.coords(parent) + parent_x = parent_coords[0] + (parent_coords[2] - parent_coords[0]) // 2 + parent_y = parent_coords[1] + (parent_coords[3] - parent_coords[1]) // 2 + self.create_line(parent_x, parent_y + self.node_height // 2, x, y, fill="black") + self.update() + return node_id + + def draw_expression(self, expression, x, y, parent=None, sibling_width=0): + # 创建节点并绘制表达式文本 + node = self.add_node(str(expression), x, y, parent=parent) + if expression.is_Atom: + return node + # 处理子表达式 + num_children = len(expression.args) + total_width = num_children * self.node_width + (num_children - 1) * self.x_spacing + start_x = x - total_width // 2 + for subexpr in expression.args: + subnode = self.draw_expression(subexpr, start_x, y + self.y_spacing, parent=node, sibling_width=total_width) + start_x += self.node_width + self.x_spacing + return node + + +class FunctionDisplay(Frame): + def __init__(self, master, attr): + super().__init__(master) + self.attr = attr + self.font_style = tkFont.Font(family="Lucida Grande", size=30) + self.functions = FunctionUtil() + self.master = master + self.create_window() + + def add_function(self): + """ + 用户添加函数 + """ + input_func = self.func_input.get() + if input_func == "": + messagebox.showwarning("注意", message="请输入函数！") + return + elif input_func.find("=") < 0: + messagebox.showerror("注意", message="添加函数的格式为：\nSinPlusCos(x)=sin(x)+cos(x)") + return + left_var = input_func.split("=")[0] + right_var = input_func.split("=")[1] + try: + function = self.functions.get_function_by_iter(right_var) + sympy.sympify(function, evaluate=False) + except Exception as E: + messagebox.showerror("注意", message="函数解析错误，请仔细检查函数是否正确！") + self.func_input.delete(0, END) + return + if self.functions.check_function_exit(left_var): + result = messagebox.askokcancel(title='标题~', message=f'函数{left_var}已经存在，是否需要覆盖！') + if result: + self.functions.add_function(left_var, right_var) + messagebox.showinfo(title="提示", message="覆盖成功！") + self.func_input.delete(0, END) + return + self.functions.add_function(left_var, right_var) + messagebox.showinfo(title="提示", message="添加成功！") + self.func_input.delete(0, END) + + def update_quadrant(self): + """ + 更换象限 + """ + self.axis_canvas.switch_quadrant(self.quadrant.get()) + self.print_function() + + def print_function(self): + """ + 输出 + """ + input_func = self.func_input.get() + if input_func == "": + messagebox.showwarning("注意", message="请输入函数！") + return + step = eval(self.x_step.get()) if not self.x_step.get() == "" else 0.1 + count = self.x_count.get() if not self.x_count.get() == "" else None + x_scale = self.x_scale.get() if not self.x_scale.get() == "" else 20 + y_scale = self.y_scale.get() if not self.y_scale.get() == "" else 40 + if input_func.find("=") >= 0: + left_var = input_func.split("=")[0] + right_var = input_func.split("=")[1] + if self.functions.check_function_exit(right_var): + func = self.functions.get_function_by_iter(right_var) + self.axis_canvas.draw_graph(func, step, count, + x_scale, y_scale) + else: + self.axis_canvas.draw_graph(input_func, step, count, + x_scale, y_scale) + else: + if self.functions.check_function_exit(input_func): + func = self.functions.get_function_by_iter(input_func) + self.axis_canvas.draw_graph(func, step, count, + x_scale, y_scale) + else: + self.axis_canvas.draw_graph(input_func, step, count, + x_scale, y_scale) + + def create_form(self): + bottom_frame = Frame(self.master, width=self.attr["width"], height=self.attr["height"] * 0.3) + self.func_input = Entry(bottom_frame, font=self.font_style, width=40) + self.func_input.grid(row=0, column=0, columnspan=4, padx=30) + self.add_func_button = Button(bottom_frame, text="用户命名并新增基本函数", command=self.add_function) + self.add_func_button.grid(row=0, column=4, padx=10) + Label(bottom_frame, text="x步长", font=("Lucida Grande", 20)).grid(row=1, column=0, padx=30) + self.x_step = Entry(bottom_frame, font=self.font_style, width=10) + self.x_step.grid(row=1, column=1, padx=10, pady=10) + Label(bottom_frame, text="x个数", font=("Lucida Grande", 20)).grid(row=1, column=2, padx=30) + self.x_count = Entry(bottom_frame, font=self.font_style, width=10) + self.x_count.grid(row=1, column=3, padx=10, pady=10) + + Label(bottom_frame, text="坐标轴", font=("Lucida Grande", 20)).grid(row=2, column=0, padx=30) + self.quadrant = IntVar() + self.quadrant.set(4) + Radiobutton(bottom_frame, text="四象限", command=self.update_quadrant, value=4, variable=self.quadrant).grid(row=2, column=1, padx=10, pady=10) + Radiobutton(bottom_frame, text="一象限", command=self.update_quadrant, value=1, variable=self.quadrant).grid(row=2, column=2, padx=10, pady=10) + + Label(bottom_frame, text="x放大倍数", font=("Lucida Grande", 20)).grid(row=3, column=0, padx=30) + self.x_scale = Entry(bottom_frame, font=self.font_style, width=10) + self.x_scale.grid(row=3, column=1, padx=10, pady=10) + Label(bottom_frame, text="y放大倍数", font=("Lucida Grande", 20)).grid(row=3, column=2, padx=30) + self.y_scale = Entry(bottom_frame, font=self.font_style, width=10) + self.y_scale.grid(row=3, column=3, padx=10, pady=10) + + Button(bottom_frame, text="输出", + command=self.print_function, width=5).grid(row=1, rowspan=3, column=4, sticky="w") + bottom_frame.place(x=0, y=self.attr["height"] * 0.65 + 20) + + def show_user_function(self): + children_window = Toplevel(root) + children_window.title("用户自定义函数") + children_window.geometry('350x260+450+200') + packet_frame = Frame(children_window) + packet_frame.grid(row=0, column=0, columnspan=3, padx=10, pady=5) + function_treeview = Treeview(packet_frame, columns=("function_name", "function"), show="headings") + function_treeview.heading("function_name", text="函数名称") + function_treeview.column("function_name", width=100, anchor=CENTER) + function_treeview.heading("function", text="函数体") + function_treeview.column("function", width=200, anchor=CENTER) + function_treeview.pack(side="left", fill="both") + scrollbar = Scrollbar(packet_frame, orient="vertical", command=function_treeview.yview) + scrollbar.pack(side="right", fill="y") + function_treeview.configure(yscrollcommand=scrollbar.set) + + def delete_item(): + selected_item = function_treeview.selection() + for item in selected_item: + item_data = function_treeview.item(item) + function_treeview.delete(item) + self.functions.data.pop(item_data["values"][0]) + self.functions.save() + + context_menu = Menu(root, tearoff=False) + context_menu.add_command(label="删除", command=delete_item) + + def popup_menu(event): + if function_treeview.identify_region(event.x, event.y) == "cell": + function_treeview.selection_set(function_treeview.identify_row(event.y)) + context_menu.post(event.x_root, event.y_root) + + function_treeview.bind("", popup_menu) + for function_name, function in self.functions.data.items(): + function_treeview.insert("", "end", values=(function_name, function)) + + + def create_window(self): + self.axis_canvas = Graph(self.master, width=self.attr["width"] * 0.65, height=self.attr["height"] * 0.65, bg="#cdcdcd") + self.axis_canvas.place(x=0, y=0) + self.text_canvas = ExpressionCanvas(self.master, width=self.attr["width"] * 0.35, height=self.attr["height"] * 0.65, bg="#cdcdcd") + self.text_canvas.create_text(20 + 180, 35, text='可识别基本函数', fill='red', font=("Purisa", 25, "bold")) + menubar = Menu(root) + menubar.add_command(label='查看自定义函数', command=self.show_user_function) + root.config(menu=menubar) + text = "可支持下列函数的加减乘除组合运算\n" \ + "\ty=sin(x)\n" \ + "\tcos(x)\n" \ + "\ttan(x)\n" \ + "\tcot(x)\n" \ + "\tx^n\n" \ + "\tP1(x)=x^3+x^2+x+5\n" \ + "---将括号内的表达式命名为P1,P1可\n" \ + "出现于用户构造中" + self.text_canvas.create_text(20 + 180, 35, text='可识别基本函数', fill='red', font=("Purisa", 25, "bold")) + center_text(self.text_canvas, text, ("Lucida Grande", 17)) + self.text_canvas.place(x=int(self.attr["width"] * 0.65), y=0) + self.create_form() + + +if __name__ == '__main__': + root = Window() + screenwidth = root.winfo_screenwidth() + screenheight = root.winfo_screenheight() + root_attr = { + "width": 1200, + "height": 800, + } + alignstr = '%dx%d+%d+%d' % (root_attr['width'], root_attr['height'], (screenwidth - root_attr['width']) / 2, + (screenheight - root_attr['height']) / 2) + root.geometry(alignstr) + root.resizable(width=False, height=False) + app = FunctionDisplay(root, root_attr) + ttk.Style().configure("TButton", font="-size 18") + ttk.Style().configure("TRadiobutton", font="-size 18") + root.mainloop() diff --git a/x3/function.json b/x3/function.json new file mode 100644 index 0000000..8c369d5 --- /dev/null +++ b/x3/function.json @@ -0,0 +1 @@ +{"f1": "x**2 + 2*x + 1", "f3": "x**2", "f2": "(x/100)**2+2*(x/100)+1", "sinpluscos(x)": "cos(x) + sin(x)"} \ No newline at end of file diff --git a/x3/functionUtil.py b/x3/functionUtil.py new file mode 100644 index 0000000..09e52e3 --- /dev/null +++ b/x3/functionUtil.py @@ -0,0 +1,57 @@ +import json +import re + + +class FunctionUtil: + def __init__(self): + self.filename = "./function.json" + self.data = {} + self.load() + + def load(self): + """ + 加载文件数据 + """ + try: + with open(self.filename, 'r', encoding="utf-8") as f: + self.data = json.load(f) + except FileNotFoundError: + pass + + def save(self): + """ + 将函数保存至json文件当中 + """ + with open(self.filename, "w", encoding="utf-8") as f: + json.dump(self.data, f) + + def check_function_exit(self, function): + """ + 检查用户输入的函数是否包含用户自定义函数 + """ + for key in self.data.keys(): + if function.find(key) >=0: + return True + return False + + def add_function(self, key, value): + """ + 添加函数 + """ + self.data[key.strip()] = value.strip() + self.save() + + def get_function_by_iter(self, key): + result = key + for dict_key in self.data.keys(): + if result.find(dict_key) >= 0: + value = result.replace(dict_key, self.data[dict_key]) + result = self.replace_values_recursive(value) + return result + + def replace_values_recursive(self, value): + for key in self.data: + if key in value: + replacement = self.data[key] + value = value.replace(key, replacement) + return value diff --git a/x3/test.py b/x3/test.py new file mode 100644 index 0000000..b81dcd4 --- /dev/null +++ b/x3/test.py @@ -0,0 +1,9 @@ +import sympy + +from functionUtil import FunctionUtil + + +# f = FunctionUtil() +# print(f.get_function_by_iter("f1 + f3")) + +print(sympy.sympify("(x/100)**2+2*(x/100)+1")) \ No newline at end of file diff --git a/x3/x3_210.py b/x3/x3_210.py new file mode 100644 index 0000000..a45d68b --- /dev/null +++ b/x3/x3_210.py @@ -0,0 +1,25 @@ +def trapezoidal_rule(a, b, n): + """ + 梯形法进行数值积分 + + 参数: + - f: 要积分的函数 + - a: 积分区间的起始点 + - b: 积分区间的结束点 + - n: 划分的子区间数 + + 返回: + - 积分近似值 + """ + h = (b - a) / n # 子区间宽度 + x = [a + i * h for i in range(n+1)] # 子区间的节点 + y = [x_i ** 2 for x_i in x] # 子区间节点对应的函数值 + integral = (h / 2) * (y[0] + 2 * sum(y[1:n]) + y[n]) # 梯形法计算积分值 + return integral + +if __name__ == '__main__': + a = 0 # 积分区间的起始点 + b = 1 # 积分区间的结束点 + n = 100 # 划分的子区间数 + integral = trapezoidal_rule(a, b, n) + print("数值积分的近似值:", integral) \ No newline at end of file diff --git a/x3/x3_211.py b/x3/x3_211.py new file mode 100644 index 0000000..4ad9a00 --- /dev/null +++ b/x3/x3_211.py @@ -0,0 +1,25 @@ +def central_difference(f, x, h): + """ + 中心差分法进行数值微分（计算导数） + + 参数: + - f: 要求导数的函数 + - x: 求导点的横坐标 + - h: 步长 + + 返回: + - 导数的近似值 + """ + df = (f(x + h) - f(x - h)) / (2 * h) # 中心差分法计算导数 + + return df + +def f(x): + return x**2 + +if __name__ == '__main__': + x = 2 # 求导点的横坐标 + h = 0.01 # 步长 + + df = central_difference(f, x, h) + print("导数的近似值:", df) \ No newline at end of file diff --git a/x3/x3_212.py b/x3/x3_212.py new file mode 100644 index 0000000..0ec7378 --- /dev/null +++ b/x3/x3_212.py @@ -0,0 +1,39 @@ +def newton_method(f, f_prime, x0, tol=1e-6, max_iter=100): + """ + 牛顿迭代法计算函数值为0的解 + + 参数: + - f: 要求解的函数 + - f_prime: 函数的导数 + - x0: 初始猜测值 + - tol: 容差（迭代停止的条件，可选，默认为1e-6） + - max_iter: 最大迭代次数（可选，默认为100） + + 返回: + - 解的近似值 + """ + x = x0 # 初始猜测值 + for _ in range(max_iter): + fx = f(x) # 函数值 + if abs(fx) < tol: + # 已达到容差要求，返回解的近似值 + return x + fpx = f_prime(x) # 函数的导数值 + if abs(fpx) < tol: + # 导数值过小，无法继续迭代 + break + x -= fx / fpx # 牛顿迭代公式 + # 迭代未收敛或超过最大迭代次数，返回None表示未找到解 + return None + +def f(x): + return x**2 - 4 + +def f_prime(x): + return 2 * x + + +if __name__ == '__main__': + x0 = 1 # 初始猜测值 + solution = newton_method(f, f_prime, x0) + print("解的近似值:", solution) \ No newline at end of file diff --git a/x4/FunctionDisplay_X4.py b/x4/FunctionDisplay_X4.py new file mode 100644 index 0000000..5ba9baf --- /dev/null +++ b/x4/FunctionDisplay_X4.py @@ -0,0 +1,400 @@ +import math +from collections import OrderedDict +from time import sleep +from ttkbootstrap import * +import tkinter.font as tkFont +from tkinter import messagebox +from tkinter.ttk import Treeview + +import sympy +from numpy import arange +from functionUtil import FunctionUtil + + +# 获取文本的宽度和高度 +def get_text_dimensions(canvas, text, font): + text_id = canvas.create_text(0, 0, text=text, font=font, anchor="center") + bbox = canvas.bbox(text_id) + width = bbox[2] - bbox[0] + height = bbox[3] - bbox[1] + canvas.delete(text_id) + return width, height + + +# 在画布中央绘制文本 +def center_text(canvas, text, font): + canvas_width = int(canvas.cget("width")) + text_width, text_height = get_text_dimensions(canvas, text, font) + x = canvas_width // 2 + y = 200 + canvas.create_text(x, y, text=text, font=font, anchor="center") + + +class Graph(Canvas): + def __init__(self, master=None, **kwargs): + super().__init__(master, **kwargs) + self.width = int(self.cget('width')) + self.height = int(self.cget('height')) + self.origin = (self.width / 2, self.height / 2) + self.bili_x = 20 + self.bili_y = 20 + self.draw_axis() + self.draw_scale() + + def draw_axis(self): + """ + 绘制坐标轴 + """ + self.delete("all") + self.create_line(0, self.origin[1], self.width, self.origin[1], fill='black', arrow=LAST) # 一象限xy轴 + self.create_line(self.origin[0], 0, self.origin[0], self.height, fill='black', arrow=FIRST) + + def draw_scale(self): + """ + 绘制刻度值 + """ + for i in range(-math.ceil((self.origin[0] / self.bili_x)) + 1, math.ceil((self.width - self.origin[0]) / self.bili_x)):#将画布x轴每20个像素点作为一个刻度，i向上取整代表刻度值 + j = i * self.bili_x #j代表的是i刻度值这一点的像素值 + if (i % 10 == 0):#如果刻度值是十的倍数 + self.create_line(j + self.origin[0], self.origin[1], j + self.origin[0], self.origin[1] - 5, fill='black') + self.create_text(j + self.origin[0], self.origin[1] + 10, text=i) + for i in range(-math.ceil((self.height - self.origin[1]) / self.bili_y) + 1, math.ceil((self.origin[1] / self.bili_y))):#将画布y轴每20个像素点作为一个刻度，i向上取整代表刻度值 + j = -(i * self.bili_y) + if (i == 0):#不重复写零点 + continue + elif (i % 2 == 0): + self.create_line(self.origin[0], j + self.origin[1], self.origin[0] + 5, j + self.origin[1], fill='black') + self.create_text(self.origin[0] - 10, j + self.origin[1], text=i) + + def switch_quadrant(self, quadrant): + """ + 切换象限 + """ + if quadrant == 1: + self.origin = (50, self.height - 50) + else: + self.origin = (self.width / 2, self.height / 2) + self.draw_axis() + self.draw_scale() + + def get_xy(self): + return -math.ceil((self.origin[0] / self.bili_x)) + 1, math.ceil((self.width - self.origin[0]) / self.bili_x) + + def draw_graph(self, func, draw_precision=0.1, count=1000, bili_x=20, bili_y=40, c='blue'): + 'xmin,xmax 自变量的取值范围； c 图像颜色' + 'x0,y0 原点坐标 w,h 横纵轴半长 draw_precision 步进' + self.bili_x, self.bili_y = int(bili_x), int(bili_y) + self.draw_axis() + self.draw_scale() + w1, w2 = self.bili_x, self.bili_y # w1,w2为自变量和函数值在横纵轴上的放大倍数 + xmin, xmax = self.get_xy() + co2 = [] + try: + for x in arange(xmin, xmax, draw_precision): # draw_precision----画图精度 + y = sympy.sympify(func, convert_xor=True).subs("x", x).evalf() + coord = self.origin[0] + w1 * x, self.origin[1] - w2 * y, self.origin[0] + w1 * x + 1, self.origin[1] - w2 * y + 1 + if abs(coord[1]) < self.height: # 超过w,h就截断 + co2.append((self.origin[0] + w1 * x, self.origin[1] - w2 * y)) + if count is None: + length = len(co2) + else: + length = len(co2[:int(count)]) + for i in range(length): + if (draw_precision >= 1): + self.create_line(co2, fill=c, width=1) + if (i + 1 == len(co2)): + break + if (abs(co2[i][1] - co2[i + 1][1]) > 100): + continue + else: + self.create_line(co2[i], co2[i + 1], fill=c, width=1) + sleep(0.01) + self.update() + except Exception as E: + messagebox.showerror("错误", message=f"函数有误!\n{E}") + + +class ExpressionCanvas(Canvas): + def __init__(self, master, *args, **kwargs): + super().__init__(master, *args, **kwargs) + self.node_width = 60 + self.node_height = 30 + self.x_spacing = 10 + self.y_spacing = 70 + self.level = {} + + def add_node(self, text, x, y, parent=None): + node_width = len(text) * 5 + 20 + if node_width < 40: + node_width = 50 + # 创建节点 + coords = [x - node_width / 2, y, x + node_width / 2, y + self.node_height] + if coords[1] in self.level: + max_x = max(self.level[coords[1]]) + if coords[0] <= max_x: + x = max_x + node_width / 2 + self.x_spacing + node_id = self.create_rectangle(x - node_width / 2, y, x + node_width / 2, y + self.node_height, + fill="white") + sleep(0.2) + self.update() + elif text == "x": + x = self.coords(parent)[0] + node_width / 2 + node_id = self.create_rectangle(x - node_width / 2, y, x + node_width / 2, y + self.node_height, + fill="white") + sleep(0.2) + self.update() + else: + node_id = self.create_rectangle(x - node_width / 2, y, x + node_width / 2, y + self.node_height, fill="white") + sleep(0.2) + self.update() + coords = [x - node_width / 2, y, x + node_width / 2, y + self.node_height] + if coords[1] in self.level: + self.level[coords[1]].append(coords[2]) + else: + self.level[coords[1]] = [coords[2]] + text_id = self.create_text(x + 5, y + self.node_height // 2, text=text, anchor="center") + sleep(0.2) + self.update() + # 绘制父节点和当前节点的连线 + if parent: + parent_coords = self.coords(parent) + parent_x = parent_coords[0] + (parent_coords[2] - parent_coords[0]) // 2 + parent_y = parent_coords[1] + (parent_coords[3] - parent_coords[1]) // 2 + self.create_line(parent_x, parent_y + self.node_height // 2, x, y, fill="black") + self.update() + return node_id + + def draw_expression(self, expression, x, y, parent=None, sibling_width=0): + # 创建节点并绘制表达式文本 + node = self.add_node(str(expression), x, y, parent=parent) + if expression.is_Atom: + return node + # 处理子表达式 + num_children = len(expression.args) + total_width = num_children * self.node_width + (num_children - 1) * self.x_spacing + start_x = x - total_width // 2 + for subexpr in expression.args: + subnode = self.draw_expression(subexpr, start_x, y + self.y_spacing, parent=node, sibling_width=total_width) + start_x += self.node_width + self.x_spacing + return node + + +class FunctionDisplay(Frame): + def __init__(self, master, attr): + super().__init__(master) + self.attr = attr + self.font_style = tkFont.Font(family="Lucida Grande", size=30) + self.functions = FunctionUtil() + self.master = master + self.create_window() + + def clear_text_canvas(self, event): + def clear_text(): + self.text_canvas.delete("all") + self.text_canvas.create_text(20 + 180, 20, text='可识别基本函数', fill='red', font=("Purisa", 25, "bold")) + center_text(self.text_canvas, self.text, ("Lucida Grande", 15)) + self.menu = Menu(self, tearoff=False) + self.menu.add_command(label="重置", command=clear_text) + self.menu.post(event.x_root, event.y_root) + + def add_function(self): + """ + 用户添加函数 + """ + input_func = self.func_input.get() + if input_func == "": + messagebox.showwarning("注意", message="请输入函数！") + return + elif input_func.find("=") < 0: + messagebox.showerror("注意", message="添加函数的格式为：\nSinPlusCos(x)=sin(x)+cos(x)") + return + left_var = input_func.split("=")[0] + right_var = input_func.split("=")[1] + try: + function = self.functions.get_function_by_iter(right_var) + sympy.sympify(function, evaluate=False) + except Exception as E: + messagebox.showerror("注意", message="函数解析错误，请仔细检查函数是否正确！") + self.func_input.delete(0, END) + return + if self.functions.check_function_exit(left_var): + result = messagebox.askokcancel(title='标题~', message=f'函数{left_var}已经存在，是否需要覆盖！') + if result: + self.functions.add_function(left_var, right_var) + messagebox.showinfo(title="提示", message="覆盖成功！") + self.func_input.delete(0, END) + return + self.functions.add_function(left_var, right_var) + messagebox.showinfo(title="提示", message="添加成功！") + self.func_input.delete(0, END) + + def update_quadrant(self): + """ + 更换象限 + """ + self.axis_canvas.switch_quadrant(self.quadrant.get()) + self.print_function() + + def print_function(self): + """ + 输出 + """ + self.text_canvas.delete("all") + self.text_canvas.level.clear() + input_func = self.func_input.get() + if input_func == "": + messagebox.showwarning("注意", message="请输入函数！") + return + step = eval(self.x_step.get()) if not self.x_step.get() == "" else 0.1 + count = self.x_count.get() if not self.x_count.get() == "" else None + x_scale = self.x_scale.get() if not self.x_scale.get() == "" else 20 + y_scale = self.y_scale.get() if not self.y_scale.get() == "" else 40 + if input_func.find("=") >= 0: + left_var = input_func.split("=")[0] + right_var = input_func.split("=")[1] + if self.functions.check_function_exit(right_var): + func = self.functions.get_function_by_iter(right_var) + self.axis_canvas.draw_graph(func, step, count, + x_scale, y_scale) + self.text_canvas.draw_expression(sympy.sympify(func, evaluate=False, convert_xor=True), int(self.text_canvas.cget("width")) // 2, self.text_canvas.y_spacing) + else: + self.axis_canvas.draw_graph(right_var, step, count, + x_scale, y_scale) + self.text_canvas.draw_expression(sympy.sympify(right_var, evaluate=False, convert_xor=True), int(self.text_canvas.cget("width")) // 2, self.text_canvas.y_spacing) + else: + if self.functions.check_function_exit(input_func): + func = self.functions.get_function_by_iter(input_func) + self.axis_canvas.draw_graph(func, step, count, + x_scale, y_scale) + self.text_canvas.draw_expression(sympy.sympify(func, evaluate=False, convert_xor=True), int(self.text_canvas.cget("width")) // 2, self.text_canvas.y_spacing) + else: + self.axis_canvas.draw_graph(input_func, step, count, + x_scale, y_scale) + self.text_canvas.draw_expression(sympy.sympify(input_func, evaluate=False, convert_xor=True), int(self.text_canvas.cget("width")) // 2, self.text_canvas.y_spacing) + + def create_form(self): + bottom_frame = Frame(self.master, width=self.attr["width"], height=self.attr["height"] * 0.3) + self.func_input = Entry(bottom_frame, font=self.font_style, width=40) + self.func_input.grid(row=0, column=0, columnspan=4, padx=30) + self.add_func_button = Button(bottom_frame, text="用户命名并新增基本函数", command=self.add_function) + self.add_func_button.grid(row=0, column=4, padx=10) + Label(bottom_frame, text="x步长", font=("Lucida Grande", 20)).grid(row=1, column=0, padx=30) + self.x_step = Entry(bottom_frame, font=self.font_style, width=10) + self.x_step.grid(row=1, column=1, padx=10, pady=10) + Label(bottom_frame, text="x个数", font=("Lucida Grande", 20)).grid(row=1, column=2, padx=30) + self.x_count = Entry(bottom_frame, font=self.font_style, width=10) + self.x_count.grid(row=1, column=3, padx=10, pady=10) + + Label(bottom_frame, text="坐标轴", font=("Lucida Grande", 20)).grid(row=2, column=0, padx=30) + self.quadrant = IntVar() + self.quadrant.set(4) + Radiobutton(bottom_frame, text="四象限", command=self.update_quadrant, value=4, variable=self.quadrant).grid(row=2, column=1, padx=10, pady=10) + Radiobutton(bottom_frame, text="一象限", command=self.update_quadrant, value=1, variable=self.quadrant).grid(row=2, column=2, padx=10, pady=10) + + Label(bottom_frame, text="x放大倍数", font=("Lucida Grande", 20)).grid(row=3, column=0, padx=30) + self.x_scale = Entry(bottom_frame, font=self.font_style, width=10) + self.x_scale.grid(row=3, column=1, padx=10, pady=10) + Label(bottom_frame, text="y放大倍数", font=("Lucida Grande", 20)).grid(row=3, column=2, padx=30) + self.y_scale = Entry(bottom_frame, font=self.font_style, width=10) + self.y_scale.grid(row=3, column=3, padx=10, pady=10) + + Button(bottom_frame, text="输出", + command=self.print_function, width=5).grid(row=1, rowspan=3, column=4, sticky="w") + bottom_frame.place(x=0, y=self.attr["height"] * 0.65 + 20) + + def show_user_function(self): + children_window = Toplevel(root) + children_window.title("用户自定义函数") + children_window.geometry('350x260+450+200') + packet_frame = Frame(children_window) + packet_frame.grid(row=0, column=0, columnspan=3, padx=10, pady=5) + function_treeview = Treeview(packet_frame, columns=("function_name", "function"), show="headings") + function_treeview.heading("function_name", text="函数名称") + function_treeview.column("function_name", width=100, anchor=CENTER) + function_treeview.heading("function", text="函数体") + function_treeview.column("function", width=200, anchor=CENTER) + function_treeview.pack(side="left", fill="both") + scrollbar = Scrollbar(packet_frame, orient="vertical", command=function_treeview.yview) + scrollbar.pack(side="right", fill="y") + function_treeview.configure(yscrollcommand=scrollbar.set) + + def delete_item(): + selected_item = function_treeview.selection() + for item in selected_item: + item_data = function_treeview.item(item) + function_treeview.delete(item) + self.functions.data.pop(item_data["values"][0]) + self.functions.save() + + context_menu = Menu(root, tearoff=False) + context_menu.add_command(label="删除", command=delete_item) + + def popup_menu(event): + if function_treeview.identify_region(event.x, event.y) == "cell": + function_treeview.selection_set(function_treeview.identify_row(event.y)) + context_menu.post(event.x_root, event.y_root) + + function_treeview.bind("", popup_menu) + for function_name, function in self.functions.data.items(): + function_treeview.insert("", "end", values=(function_name, function)) + + def create_window(self): + self.axis_canvas = Graph(self.master, width=self.attr["width"] * 0.65, height=self.attr["height"] * 0.65, bg="#cdcdcd") + self.axis_canvas.place(x=0, y=0) + self.text_canvas = ExpressionCanvas(self.master, width=self.attr["width"] * 0.35, height=self.attr["height"] * 0.65, bg="#cdcdcd") + menubar = Menu(root) + menubar.add_command(label='查看自定义函数', command=self.show_user_function) + root.config(menu=menubar) + # self.text = "可支持下列函数的加减乘除组合运算\n" \ + # "常用运算符：+,-,*,/,**,//,%\n" \ + # "常用函数：\n" \ + # " sqrt(x)：求平方根\n" \ + # "数学常数：\n" \ + # " 虚数单位：I\n" \ + # " 自然对数的底：E\n" \ + # " 无穷大：oo\n" \ + # " 圆周率：pi\n" \ + # "三角函数：sin(x),cos(x),tan(x)\n" \ + # " sec(x),csc(x),cot(x),sinc(x)\n" \ + # " 及其反函数：sinh(),cosh()等\n" \ + # "复杂函数：\n" \ + # " 伽马函数：gamma(x)\n" \ + # " 贝塔函数：beta()\n" \ + # " 误差函数：erf(x)\n" \ + # "指数运算：\n" \ + # " 指数运算：exp()\n" \ + # " 自然对数：log()\n" \ + # " 以十为底的对数：log(var, 10)\n" \ + # " 自然对数：ln()或log()\n" + self.text = "可支持下列函数的加减乘除组合运算\n" \ + "\ty=sin(x)\n" \ + "\tcos(x)\n" \ + "\ttan(x)\n" \ + "\tcot(x)\n" \ + "\tx^n\n" \ + "\tP1(x)=x^3+x^2+x+5\n" \ + "---将括号内的表达式命名为P1,P1可\n" \ + "出现于用户构造中" + self.text_canvas.create_text(20 + 180, 20, text='可识别基本函数', fill='red', font=("Purisa", 25, "bold")) + center_text(self.text_canvas, self.text, ("Lucida Grande", 15)) + self.text_canvas.bind("", func=self.clear_text_canvas) + self.text_canvas.place(x=int(self.attr["width"] * 0.65), y=0) + self.create_form() + + +if __name__ == '__main__': + root = Window() + screenwidth = root.winfo_screenwidth() + screenheight = root.winfo_screenheight() + root_attr = { + "width": 1200, + "height": 800, + } + alignstr = '%dx%d+%d+%d' % (root_attr['width'], root_attr['height'], (screenwidth - root_attr['width']) / 2, + (screenheight - root_attr['height']) / 2) + root.geometry(alignstr) + root.resizable(width=False, height=False) + app = FunctionDisplay(root, root_attr) + ttk.Style().configure("TButton", font="-size 18") + ttk.Style().configure("TRadiobutton", font="-size 18") + root.mainloop() diff --git a/x4/function.json b/x4/function.json new file mode 100644 index 0000000..a20339e --- /dev/null +++ b/x4/function.json @@ -0,0 +1,8 @@ +{ + "f1": "sin(x)+cos(x)+p3(x)", + "f3": "x**2", + "f2": "(x/100)**2+2*(x/100)+1", + "SinPlusCos(x)": "sin(x) + cos(x)", + "superFunc": "(x/100)**2 + 2*(x/100) + 1", + "func": "3 * x + sin(x) * cos(x)" +} \ No newline at end of file diff --git a/x4/functionUtil.py b/x4/functionUtil.py new file mode 100644 index 0000000..09e52e3 --- /dev/null +++ b/x4/functionUtil.py @@ -0,0 +1,57 @@ +import json +import re + + +class FunctionUtil: + def __init__(self): + self.filename = "./function.json" + self.data = {} + self.load() + + def load(self): + """ + 加载文件数据 + """ + try: + with open(self.filename, 'r', encoding="utf-8") as f: + self.data = json.load(f) + except FileNotFoundError: + pass + + def save(self): + """ + 将函数保存至json文件当中 + """ + with open(self.filename, "w", encoding="utf-8") as f: + json.dump(self.data, f) + + def check_function_exit(self, function): + """ + 检查用户输入的函数是否包含用户自定义函数 + """ + for key in self.data.keys(): + if function.find(key) >=0: + return True + return False + + def add_function(self, key, value): + """ + 添加函数 + """ + self.data[key.strip()] = value.strip() + self.save() + + def get_function_by_iter(self, key): + result = key + for dict_key in self.data.keys(): + if result.find(dict_key) >= 0: + value = result.replace(dict_key, self.data[dict_key]) + result = self.replace_values_recursive(value) + return result + + def replace_values_recursive(self, value): + for key in self.data: + if key in value: + replacement = self.data[key] + value = value.replace(key, replacement) + return value diff --git a/x4/test.py b/x4/test.py new file mode 100644 index 0000000..b81dcd4 --- /dev/null +++ b/x4/test.py @@ -0,0 +1,9 @@ +import sympy + +from functionUtil import FunctionUtil + + +# f = FunctionUtil() +# print(f.get_function_by_iter("f1 + f3")) + +print(sympy.sympify("(x/100)**2+2*(x/100)+1")) \ No newline at end of file diff --git a/x5/FunctionDisplay_X5.py b/x5/FunctionDisplay_X5.py new file mode 100644 index 0000000..44581bc --- /dev/null +++ b/x5/FunctionDisplay_X5.py @@ -0,0 +1,447 @@ +# -*- coding: utf-8 -*- +from time import sleep +from tkinter import * +import tkinter.font as tkFont +from tkinter import messagebox + +import numpy as np +from matplotlib.figure import Figure +from matplotlib.backends.backend_tkagg import FigureCanvasTkAgg + +import sympy +from numpy import arange +from sympy import symbols, lambdify +from functionUtil import FunctionUtil +import math +from PIL import ImageTk, Image +import sys + +# 在画布中央绘制文本 +def center_text(canvas, text, font): + canvas_width = int(canvas.cget("width")) + x = canvas_width // 2 + y = 200 + canvas.create_text(x, y, text=text, font=font, anchor="center") + + +class Graph(Canvas): + """ + 绘制函数图形 + """ + + def __init__(self, master=None, **kwargs): + super().__init__(master, **kwargs) + self.width = int(self.cget('width')) + self.height = int(self.cget('height')) + self.origin = (self.width / 2, self.height / 2) + self.config(bg="white") + self.bili_x = 20 + self.bili_y = 20 + self.draw_axis() + self.draw_scale() + self.fig = FigureCanvasTkAgg() + self.y_scale = 1.0 + + + def draw_axis(self): + """ + 绘制坐标轴 + """ + self.delete("all") + self.create_line(0, self.origin[1], self.width, self.origin[1], fill='black', arrow=LAST) # 一象限xy轴 + self.create_line(self.origin[0], 0, self.origin[0], self.height, fill='black', arrow=FIRST) + + def draw_scale(self): + """ + 绘制刻度值 + """ + for i in range(-math.ceil((self.origin[0] / self.bili_x)) + 1, + math.ceil((self.width - self.origin[0]) / self.bili_x)): + j = i * self.bili_x + if (i % 10 == 0): + self.create_line(j + self.origin[0], self.origin[1], j + self.origin[0], self.origin[1] - 5, + fill='black') + self.create_text(j + self.origin[0], self.origin[1] + 10, text=i) + for i in range(-math.ceil((self.height - self.origin[1]) / self.bili_y) + 1, + math.ceil((self.origin[1] / self.bili_y))): + j = -(i * self.bili_y) + if i == 0: + continue + elif i % 2 == 0: + self.create_line(self.origin[0], j + self.origin[1], self.origin[0] + 5, j + self.origin[1], + fill='black') + self.create_text(self.origin[0] - 10, j + self.origin[1], text=i) + + def switch_quadrant(self, quadrant): + """ + 切换象限 + """ + if quadrant == 1: + self.origin = (50, self.height - 50) + else: + self.origin = (self.width / 2, self.height / 2) + self.draw_axis() + self.draw_scale() + + + def draw_graph_3d(self, func, draw_precision=0.1, count=1000, bili_x=20, bili_y=40, ): + self.fig.get_tk_widget().destroy() + self.delete("all") + # 创建 sympy 符号 + x, y = symbols('x y') + self.bili_x, self.bili_y = int(bili_x), int(bili_y) + # 将表达式转换为可计算的函数 + expr = lambdify((x, y), func, modules=['numpy']) + xmin, xmax = -math.ceil((self.origin[0] / self.bili_x)) + 1, math.ceil( + (self.width - self.origin[0]) / self.bili_x) + # 创建数据网格 + X = np.linspace(xmin, xmax, int(draw_precision * 100)) + Y = np.linspace(xmin, xmax, int(draw_precision * 100)) + X, Y = np.meshgrid(X, Y) + Z = expr(X, Y) + # 创建一个 Figure 对象 + fig = Figure(figsize=(7, 5.5), dpi=120) + # 在 Figure 上创建一个 3D 子图 + ax = fig.add_subplot(111, projection='3d') + ax.auto_scale_xyz(X, Y, Z) + # 绘制三维图形 + ax.plot_surface(X, Y, Z, cmap='viridis') + self.fig = FigureCanvasTkAgg(fig, master=self) + self.fig.draw() + self.fig.get_tk_widget().pack(fill=BOTH, ipadx=0, ipady=0, pady=0, padx=0, expand=True) + + + + + def draw_graph_2d(self, func, draw_precision=0.1, count=1000, bili_x=20, bili_y=40, c='blue'): + 'xmin,xmax 自变量的取值范围； c 图像颜色' + 'x0,y0 原点坐标 w,h 横纵轴半长 draw_precision 步进' + self.fig.get_tk_widget().destroy() + self.bili_x, self.bili_y = int(bili_x), int(bili_y) + self.draw_axis() + self.draw_scale() + w1, w2 = self.bili_x, self.bili_y # w1,w2为自变量和函数值在横纵轴上的放大倍数 + xmin, xmax = -math.ceil((self.origin[0] / self.bili_x)) + 1, math.ceil( + (self.width - self.origin[0]) / self.bili_x) + co2 = [] + try: + for x in arange(xmin, xmax, draw_precision): # draw_precision----画图精度 + y = sympy.sympify(func, convert_xor=True).subs("x", x).evalf() + coord = self.origin[0] + w1 * x, self.origin[1] - w2 * y, self.origin[0] + w1 * x + 1, self.origin[ + 1] - w2 * y + 1 + # if abs(coord[1]) < int(self.height): # 超过w,h就截断 #已经将截断注释 + co2.append((self.origin[0] + w1 * x, self.origin[1] - w2 * y)) + if count is None: + length = len(co2) + else: + length = len(co2[:int(count)]) + for i in range(length): + if (draw_precision >= 1): + self.create_line(co2, fill=c, width=1) + if (i + 1 == len(co2)): + break + if (abs(co2[i][1] - co2[i + 1][1]) > 100): + continue + else: + self.create_line(co2[i], co2[i + 1], fill=c, width=1) + # sleep(0.01) + self.update() + except Exception as E: + messagebox.showerror("错误", message=f"函数有误，错误信息如下!\n{E}") + + + def draw_graph(self,dimension,func, draw_precision=0.1, count=1000, bili_x=20, bili_y=40, ): + if dimension==1: + self.draw_graph_3d(func, draw_precision, count, bili_x, bili_y,) + else: + self.draw_graph_2d(func, draw_precision, count, bili_x, bili_y,c='blue') + +class ExpressionCanvas(Canvas): + def __init__(self, master, *args, **kwargs): + super().__init__(master, *args, **kwargs) + self.node_width = 100 + self.node_height = 40 + self.x_spacing = 15 + self.y_spacing = 70 + self.level = {} + + def add_node(self, text, x, y, parent=None): + node_width = len(text) * 15 + 20 + if node_width < 40: + node_width = 50 + # 创建节点 + coords = [x - node_width / 2, y, x + node_width / 2, y + self.node_height] + if coords[1] in self.level: + max_x = max(self.level[coords[1]]) + if coords[0] <= max_x: + x = max_x + node_width / 2 + self.x_spacing + node_id = self.create_rectangle(x - node_width / 2, y, x + node_width / 2, y + self.node_height, + fill="white") + sleep(0.2) + self.update() + elif text == "x": + x = self.coords(parent)[0] + node_width / 2 + node_id = self.create_rectangle(x - node_width / 2, y, x + node_width / 2, y + self.node_height, + fill="white") + sleep(0.2) + self.update() + else: + node_id = self.create_rectangle(x - node_width / 2, y, x + node_width / 2, y + self.node_height, + fill="white") + sleep(0.2) + self.update() + coords = [x - node_width / 2, y, x + node_width / 2, y + self.node_height] + if coords[1] in self.level: + self.level[coords[1]].append(coords[2]) + else: + self.level[coords[1]] = [coords[2]] + text_id = self.create_text(x + 5, y + self.node_height // 2, text=text, anchor="center", font=("", 15)) + sleep(0.2) + self.update() + # 绘制父节点和当前节点的连线 + if parent: + try: + parent_coords = self.coords(parent) + parent_x = parent_coords[0] + (parent_coords[2] - parent_coords[0]) // 2 + parent_y = parent_coords[1] + (parent_coords[3] - parent_coords[1]) // 2 + self.create_line(parent_x, parent_y + self.node_height // 2, x, y, fill="black") + self.update() + except Exception as E: + pass + return node_id + + def draw_expression(self, expression, x, y, parent=None, sibling_width=0): + # 创建节点并绘制表达式文本 + node = self.add_node(str(expression), x, y, parent=parent) + if expression.is_Atom: + return node + # 处理子表达式 + num_children = len(expression.args) + total_width = num_children * self.node_width + (num_children - 1) * self.x_spacing + start_x = x - total_width // 2 + for subexpr in expression.args: + subnode = self.draw_expression(subexpr, start_x, y + self.y_spacing, parent=node, sibling_width=total_width) + start_x += self.node_width + self.x_spacing + return node + + +class FunctionDisplay(Canvas): + def __init__(self, master, *args, **kwargs): + super().__init__(master, *args, **kwargs) + self.font_style = tkFont.Font(family="Lucida Grande", size=30) + self.functions = FunctionUtil() + self.width = int(self.cget("width")) + self.height = int(self.cget("height")) + self.background_img = ImageTk.PhotoImage(Image.open(sys.path[0]+"/./image/背景@3x.jpg").resize((self.width, self.height))) + self.create_image(0, 0, image=self.background_img, anchor=NW) + self.master = master + self.init_window() + self.load_user_function() + + def add_function(self): + """ + 用户添加函数 + """ + input_func = self.func_input.get() + if input_func == "": + messagebox.showwarning("注意", message="请输入函数！") + return + elif input_func.find("=") < 0: + messagebox.showerror("注意", message="添加函数的格式为：\nSinPlusCos(x)=sin(x)+cos(x)") + return + left_var = input_func.split("=")[0] + right_var = input_func.split("=")[1] + try: + function = self.functions.get_function_by_iter(right_var) + sympy.sympify(function, evaluate=False) + except Exception as E: + messagebox.showerror("注意", message="函数解析错误，请仔细检查函数是否正确！") + self.func_input.delete(0, END) + return + if self.functions.check_function_exit(left_var): + result = messagebox.askokcancel(title='提示', message=f'函数{left_var}已经存在，是否需要覆盖！') + if result: + self.functions.add_function(left_var, right_var) + messagebox.showinfo(title="提示", message="覆盖成功！") + self.func_input.delete(0, END) + self.load_user_function() + return + self.functions.add_function(left_var, right_var) + messagebox.showinfo(title="提示", message="添加成功！") + self.func_input.delete(0, END) + self.load_user_function() + + def update_dimension(self): + """ + 更换维度 + """ + dimension=self.dimension.get() + self.print_function() + + def update_quadrant(self): + """ + 更换象限 + """ + self.axis_canvas.switch_quadrant(self.quadrant.get()) + self.print_function() + + def print_function(self): + """ + 输出 + """ + dimension=self.dimension.get() + self.text_canvas.delete("all") + self.text_canvas.level.clear() + input_func = self.func_input.get() + if input_func == "": + messagebox.showwarning("注意", message="请输入函数！") + return + step = eval(self.x_step.get()) if not self.x_step.get() == "" else 0.1 + count = self.x_count.get() if not self.x_count.get() == "" else None + x_scale = int(self.x_scale.get())*20 if not self.x_scale.get() == "" else 20 + y_scale = int(self.y_scale.get())*40 if not self.y_scale.get() == "" else 40 + if input_func.find("=") >= 0: + input_func = input_func.split("=")[1] + if self.functions.check_function_exit(input_func): + func = self.functions.get_function_by_iter(input_func) + self.axis_canvas.draw_graph(dimension,func, step, count, x_scale, y_scale) + self.text_canvas.draw_expression(sympy.sympify(func, evaluate=False, convert_xor=True), + int(self.text_canvas.cget("width")) // 2, self.text_canvas.y_spacing) + else: + self.axis_canvas.draw_graph(dimension,input_func, step, count, x_scale, y_scale) + self.text_canvas.draw_expression(sympy.sympify(input_func, evaluate=False, convert_xor=True), + int(self.text_canvas.cget("width")) // 2, self.text_canvas.y_spacing) + + def load_user_function(self): + self.user_function_canvas.delete(ALL) + self.user_function_canvas.create_text(20 + 90, 35, text='可识别基本函数', fill='red', + font=("Purisa", 20, "bold")) + num = 2 + self.user_function_canvas.create_text(0, 70, anchor="nw", text="函数名", font=("", 15)) + self.user_function_canvas.create_text(150, 70, anchor="nw", text="函数体", font=("", 15)) + for function, function_body in self.functions.data.items(): + self.user_function_canvas.create_text(0, 20 * num + 50, anchor="nw", text=function, font=("", 15)) + self.user_function_canvas.create_text(150, 20 * num + 50, anchor="nw", text=function_body, font=("", 15)) + num += 1 + self.user_function_canvas.update() + self.user_function_canvas.configure(scrollregion=self.user_function_canvas.bbox("all")) + + def create_form(self): + bottom_frame = Canvas(self, width=self.width, height=self.height * 0.3, highlightthickness=0) + self.back_image = ImageTk.PhotoImage(Image.open(sys.path[0]+"/./image/下部背景@3x.png").resize((self.width, int(self.height * 0.3)))) + bottom_frame.create_image(0, 0, image=self.back_image, anchor=NW) + label_width, entry_width, label_margin_left, margin_left, height, margin_top = 100, 215, 120 + 50, 120, 42, 20 + self.func_input = Entry(bottom_frame, font=self.font_style) + self.func_input.place(x=margin_left, y=margin_top, anchor=NW, width=1000, height=height) + self.add_func_image = ImageTk.PhotoImage(Image.open(sys.path[0]+"/./image/用户命名并新增基本函数@3x.png").resize((180, 62))) + self.add_func_button = Button(bottom_frame, image=self.add_func_image, bd=0, relief="solid", bg="#f7f7f7", + highlightthickness=0, command=self.add_function) + self.add_func_button.place(x=1140, y=10, anchor=NW) + + self.label_img = ImageTk.PhotoImage(Image.open(sys.path[0]+"/./image/文字背景@3x.png").resize((100, 42))) + bottom_frame.create_image(label_margin_left-100, 112, image=self.label_img) + bottom_frame.create_text(label_margin_left-100, 112, text="x步长", fill="white", font=("", 20)) + self.x_step = Entry(bottom_frame, font=self.font_style) + self.x_step.place(x=margin_left + label_width-100, y=112 - 21, width=215, height=42) + + self.label1_img = ImageTk.PhotoImage(Image.open(sys.path[0]+"/./image/文字背景@3x.png").resize((100, 42))) + bottom_frame.create_image(label_margin_left-100, 171, image=self.label1_img) + bottom_frame.create_text(label_margin_left-100, 170, text="x个数", fill="white", font=("", 20)) + self.x_count = Entry(bottom_frame, font=self.font_style) + self.x_count.place(x=margin_left + label_width-100, y=112 + 39, width=215, height=42) + + self.big_label_img = ImageTk.PhotoImage(Image.open(sys.path[0]+"/./image/文字背景2@3x.png").resize((label_width+5, height * 2 + margin_top))) + bottom_frame.create_image(label_margin_left + label_width + entry_width - 80, 112 + 31, image=self.big_label_img) + bottom_frame.create_text(label_margin_left + label_width + entry_width - 80, 112 + 31, text="坐标轴", fill="white", font=("", 25)) + self.quadrant = IntVar() + self.quadrant.set(4) + Radiobutton(bottom_frame, text="四象限", command=self.update_quadrant, font=("", 17), + bg="#b9b9f7",highlightthickness=0, highlightcolor="#aaaaf2", + value=4, variable=self.quadrant).place(x=label_margin_left + label_width * 2 + entry_width -128, y=90, + height=(height * 2 + margin_top) / 2, width=entry_width, anchor=NW) + Radiobutton(bottom_frame, text="一象限", command=self.update_quadrant, font=("", 17), bg="#b9b9f7", + highlightthickness=0, highlightcolor="#aaaaf2", + value=1, variable=self.quadrant).place(x=label_margin_left + label_width * 2 + entry_width -128, y=90 + (height * 2 + margin_top) / 2, + height=(height * 2 + margin_top) / 2, width=entry_width, anchor=NW) + + + self.big_label_img1 = ImageTk.PhotoImage(Image.open(sys.path[0]+"/./image/文字背景2@3x.png").resize((label_width+5, height * 2 + margin_top))) + bottom_frame.create_image(label_margin_left + label_width + entry_width+278, 112 + 31, image=self.big_label_img1) + bottom_frame.create_text(label_margin_left + label_width + entry_width+278, 112 + 31, text="维度", fill="white", font=("", 25)) + self.dimension = IntVar() + self.dimension.set(4) + Radiobutton(bottom_frame, text="二维", command=self.update_dimension, font=("", 17), + bg="#b9b9f7",highlightthickness=0, highlightcolor="#aaaaf2", + value=4, variable=self.dimension).place(x=label_margin_left + label_width * 2 + entry_width+230, y=90, + height=(height * 2 + margin_top) / 2, width=entry_width, anchor=NW) + Radiobutton(bottom_frame, text="三维", command=self.update_dimension, font=("", 17), bg="#b9b9f7", + highlightthickness=0, highlightcolor="#aaaaf2", + value=1, variable=self.dimension).place(x=label_margin_left + label_width * 2 + entry_width+230, y=90 + (height * 2 + margin_top) / 2, + height=(height * 2 + margin_top) / 2, width=entry_width, anchor=NW) + + + self.x_scale = Entry(bottom_frame, font=self.font_style) + self.x_scale.place(x=margin_left + label_width+100, y=112 - 21, width=215, height=42) + label_x = label_margin_left + 840 + label_y = 112 + self.label_img1 = ImageTk.PhotoImage(Image.open(sys.path[0]+"/./image/文字背景@3x.png").resize((130, 42))) + bottom_frame.create_image(label_x+100, label_y, image=self.label_img1) + bottom_frame.create_text(label_x+100, label_y, text="x放大倍数", fill="white", font=("", 20)) + entry_x = margin_left + label_width + 855 + entry_y = 112 - 21 + self.x_scale.place(x=entry_x+100, y=entry_y, width=215, height=42) + + + self.y_scale = Entry(bottom_frame, font=self.font_style) + self.y_scale.place(x=margin_left + label_width+100, y=112 - 21, width=215, height=42) + label_x = label_margin_left + 840 + label_y = 170 + bottom_frame.create_image(label_x+100, label_y, image=self.label_img1) + bottom_frame.create_text(label_x+100, label_y, text="y放大倍数", fill="white", font=("", 20)) + entry_x = margin_left + label_width + 855 + entry_y = 170 - 21 + self.y_scale.place(x=entry_x+100, y=entry_y, width=215, height=42) + + self.print_function_image = ImageTk.PhotoImage(Image.open(sys.path[0]+"/./image/输出-点击@3x.png").resize((120, 60))) + self.print_function_button = Button(bottom_frame, image=self.print_function_image, bd=0, relief="solid", bg="#f7f7f7", + highlightthickness=0, command=self.print_function) + self.print_function_button.place(x=1350, y=10, anchor=NW) + # Button(bottom_frame, text="输出", command=self.print_function, width=5) \ + # .place(x=1350, y=95, anchor=NW) + bottom_frame.place(x=0, y=self.height * 0.65 + 40, anchor=NW) + + def init_window(self): + self.axis_canvas = Graph(self, width=self.width * 0.45, height=self.height * 0.65,highlightthickness=0) + self.axis_canvas.place(x=0, y=0, anchor=NW) + self.text_canvas = ExpressionCanvas(self, width=self.width * 0.35, + height=self.height * 0.65, bg="white",highlightthickness=0) + self.text_canvas.place(x=int(self.width * 0.45), y=0) + user_function = Frame(self, width=self.width * 0.2, height=self.height * 0.65) + user_function.place(x=int(self.width * 0.8), y=0) + self.user_function_canvas = Canvas(user_function, width=self.width * 0.19, + height=self.height * 0.65, bg="white",highlightthickness=0) + y_scrollbar = Scrollbar(user_function, orient="vertical", command=self.user_function_canvas.yview) + x_scrollbar = Scrollbar(user_function, orient="horizontal", command=self.user_function_canvas.xview) + x_scrollbar.pack(side=BOTTOM, fill=BOTH) + y_scrollbar.pack(side=RIGHT, fill=BOTH) + self.user_function_canvas.pack(side=TOP, fill=BOTH) + self.user_function_canvas.config(yscrollcommand=y_scrollbar.set, xscrollcommand=x_scrollbar.set) + self.user_function_canvas.config(scrollregion=self.user_function_canvas.bbox("all")) + self.create_form() + + +if __name__ == '__main__': + root = Tk() + screenwidth = root.winfo_screenwidth() + screenheight = root.winfo_screenheight() + root_attr = { + "width": int(screenwidth * 1), + "height": int(screenheight * 1), + } + alignstr = '%dx%d+%d+%d' % (root_attr['width'], root_attr['height'], (screenwidth - root_attr['width']) / 2, + (screenheight - root_attr['height']) / 2) + root.geometry(alignstr) + root.resizable(width=False, height=False) + app = FunctionDisplay(root, width=root_attr["width"], height=root_attr["height"]) + app.place(x=0, y=0, anchor=NW) + root.mainloop() diff --git a/x5/basic.png b/x5/basic.png new file mode 100644 index 0000000..2fa5dc7 Binary files /dev/null and b/x5/basic.png differ diff --git a/x5/function.json b/x5/function.json new file mode 100644 index 0000000..a8b70c4 --- /dev/null +++ b/x5/function.json @@ -0,0 +1 @@ +{"sin(x)": "sin(x)", "cos(x)": "cos(x)", "tan(x)": "tan(x)"} \ No newline at end of file diff --git a/x5/functionUtil.py b/x5/functionUtil.py new file mode 100644 index 0000000..176e422 --- /dev/null +++ b/x5/functionUtil.py @@ -0,0 +1,63 @@ +import json +import re +import sys + +class FunctionUtil: + def __init__(self): + self.filename = sys.path[0]+"/./function.json" + self.data = {} + self.load() + + def load(self): + """ + 加载文件数据 + """ + try: + with open(self.filename, 'r', encoding="utf-8") as f: + self.data = json.load(f) + except FileNotFoundError: + pass + + def save(self): + """ + 将函数保存至json文件当中 + """ + with open(self.filename, "w", encoding="utf-8") as f: + json.dump(self.data, f) + + def check_function_exit(self, function): + """ + 检查用户输入的函数是否包含用户自定义函数 + """ + for key in self.data.keys(): + if function.find(key) >=0: + return True + return False + + def add_function(self, key, value): + """ + 添加函数 + """ + self.data[key.strip()] = value.strip() + self.save() + + def get_function_by_iter(self, key): + """ + 遍历找出函数名所对应的函数体 + """ + result = key + for dict_key in self.data.keys(): + if result.find(dict_key) >= 0: + value = result.replace(dict_key, "("+self.data[dict_key]+")") + result = self.replace_values_recursive(value) + return result + + def replace_values_recursive(self, value): + """ + 将键值对应的数学函数替换为实际函数 + """ + for key in self.data: + if key in value: + replacement = self.data[key] + value = "("+value.replace(key, replacement)+")" + return value diff --git a/x5/image/下部背景.png b/x5/image/下部背景.png new file mode 100644 index 0000000..f610758 Binary files /dev/null and b/x5/image/下部背景.png differ diff --git a/x5/image/下部背景@2x.png b/x5/image/下部背景@2x.png new file mode 100644 index 0000000..4117a49 Binary files /dev/null and b/x5/image/下部背景@2x.png differ diff --git a/x5/image/下部背景@3x.png b/x5/image/下部背景@3x.png new file mode 100644 index 0000000..ec4b13e Binary files /dev/null and b/x5/image/下部背景@3x.png differ diff --git a/x5/image/勾选.png b/x5/image/勾选.png new file mode 100644 index 0000000..1f79713 Binary files /dev/null and b/x5/image/勾选.png differ diff --git a/x5/image/勾选@2x.png b/x5/image/勾选@2x.png new file mode 100644 index 0000000..218acdd Binary files 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arange(-19, 20, 0.1) + z = [] + sympy.Symbol("x y") + for i in arange(-19, 20, 0.1): + z.append(sympy.sympify("x**2+y**2").subs("x", i).subs("y", i).evalf()) + # 在 Figure 上创建一个 3D 子图 + ax = fig.add_subplot(111, projection='3d') + ax.plot3D(x, y, z, 'gray') + + # 绘制三维图形 + # 在这里添加你自己的三维图形绘制逻辑 + # 例如 ax.plot_surface() 或 ax.scatter() + + # 创建一个 tkinter 窗口 + root = tk.Tk() + root.title("3D Graph") + + # 在 tkinter 窗口上创建一个 canvas + canvas = FigureCanvasTkAgg(fig, master=root) + canvas.draw() + canvas.get_tk_widget().pack() + + # 运行 tkinter 主循环 + tk.mainloop() + + +# 调用函数绘制三维图形 +plot_3d_graph() + + diff --git a/x5/test1.py b/x5/test1.py new file mode 100644 index 0000000..e0aa54b --- /dev/null +++ b/x5/test1.py @@ -0,0 +1,17 @@ +import tkinter as tk + + +class MyCanvas(tk.Canvas): + def __init__(self, master=None, **kwargs): + super().__init__(master, **kwargs) + + # 在画布上绘制一些文本 + self.create_text(50, 50, text="Hello, Tkinter!") + self.create_text(100, 100, text="This is a text example.") + + +if __name__ == "__main__": + root = tk.Tk() + canvas = MyCanvas(root, width=200, height=150) + canvas.pack() + root.mainloop()