upload fitt project

X1.py

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+import random
+import numpy as np
+def random_points():
+    x=[]
+    y=[]
+    for i in range(20):
+        x_= random.uniform(0, 1000)	# 生成随机浮点数
+        y_= random.uniform(0, 1000)	# 生成随机浮点数
+        x.append(x_) 	# 加入列表
+        y.append(y_)
+    x=np.array(x) 	# 列表转数组
+    y=np.array(y)
+    arr = np.array(list(zip(x, y)))	# 将两个一维数组拼接成二维数组
+    return arr
+# if __name__ == '__main__':
+#     arr = random_points()
+#     print(arr)
+
+def compute_curveData(num, step, coefficient):	# coefficient代表二次函数系数，数组形式
+    def quadratic_function(x):	                         # 构造二次函数y = a * X^2 + b * X + C
+        return coefficient[0] * x ** 2 + coefficient[1] * x + coefficient[2]
+    x_values = np.arange(0, num, step)
+    y_values = quadratic_function(x_values)		  # 调用quadratic_function(x)函数得到y值
+    curve_data = np.column_stack((x_values, y_values))  # 将两个一维数组堆叠成二维数组，形成(x,y)的形式
+    return curve_data
+if __name__ == '__main__':
+    coefficient = [1, 2, 3]
+    ans = compute_curveData(1000, 250, coefficient)
+    print(ans)

X2.py

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+from tkinter import *
+import tkinter as tk
+import mpl_toolkits.axisartist as axisartist
+import matplotlib.pyplot as plt
+from scipy.optimize import curve_fit
+import data as gl_data
+import numpy as np
+from X1 import random_points
+
+def window():
+    root_window = Tk()
+    root_window.title('函数拟合')
+
+    root_window.geometry('900x600')  # 设置窗口大小:宽x高,注,此处不能为 "*",必须使用 "x"
+    # 设置主窗口的背景颜色,颜色值可以是英文单词，或者颜色值的16进制数,除此之外还可以使用Tk内置的颜色常量
+    root_window["background"] = "white"
+    root_window.resizable(0, 0)  # 防止用户调整尺寸
+    label1 = tk.Label(root_window, text="样本数据\n集文件", font=('Times', 8), bg="white",
+                      width=13, height=3,  # 设置标签内容区大小
+                      padx=0, pady=0, borderwidth=0, )
+    label1.place(x=10, y=4)  # 设置填充区距离、边框宽度和其样式（凹陷式）
+    label3 = tk.Label(root_window, text="", font=('Times', 8), bg="white", fg="black",
+                      width=39, height=2, padx=0, pady=0, borderwidth=0, relief="ridge", highlightcolor="blue")
+    label3.place(x=122, y=10)
+    return root_window
+# if __name__ == '__main__':
+#     root_window = window()
+#     root_window.mainloop()
+
+def draw_axis(low, high, step=250):
+    fig = plt.figure(figsize=(4.4, 3.2)) # 设置显示大小
+    ax = axisartist.Subplot(fig, 111)	# 使用axisartist.Subplot方法创建一个绘图区对象ax
+    fig.add_axes(ax)   # 将绘图区对象添加到画布中
+    ax.axis[:].set_visible(False)# 通过set_visible方法设置绘图区所有坐标轴隐藏
+    ax.axis["x"] = ax.new_floating_axis(0, 0)	# 添加新的x坐标轴
+    ax.axis["x"].set_axisline_style("-|>", size=1.0) # 给x坐标轴加上箭头
+    ax.axis["y"] = ax.new_floating_axis(1, 0)	# 添加新的y坐标轴
+    ax.axis["y"].set_axisline_style("-|>", size=1.0) # y坐标轴加上箭头
+    ax.axis["x"].set_axis_direction("bottom")	# 设置x、y轴上刻度显示方向
+    ax.axis["y"].set_axis_direction("left")	# 设置x、y轴上刻度显示方向
+    plt.xlim(low, high)  # 把x轴的刻度范围设置
+    plt.ylim(low, high)  # 把y轴的刻度范围设置
+    ax.set_xticks(np.arange(low, high + 5, step))  # 把x轴的刻度间隔设置
+    ax.set_yticks(np.arange(low, high + 5, step))  # 把y轴的刻度间隔设置
+    # plt.show()
+# if __name__ == '__main__':
+#     draw_axis(-1000, 1000)
+
+def selfdata_show(sampleData):
+    num_points = len(sampleData)  	# 样本数据点的数量
+    colors = np.random.rand(num_points, 3)  # 生成随机颜色
+    draw_axis(0, 1000)
+    plt.scatter(sampleData[:, 0], sampleData[:, 1], c=colors)  # 绘制样本数据点
+    plt.show()  #显示图片
+# if __name__ == '__main__':
+#     sampleData = random_points()  # 生成样本点
+#     selfdata_show(sampleData) 	# 绘制样本数据点
+
+def quadratic_function(x, a, b, c, d):	#构造三次函数y = a * X^3 + b * X^2 + C * x + d
+    return a * x ** 3 + b * x **2 + c * x + d
+def draw_line(low, high, sx, sy):
+    draw_axis(low, high)	#绘制坐标轴
+    popt = []	#初始化curve_fit
+    pcov = []	#初始化curve_fit
+    gl_data.yvals_pow = []	#初始化curve_fit
+    popt, pcov = curve_fit(quadratic_function, sx, sy)  # 用curve_fit来对点进行拟合
+    curve_x = np.arange(low, high)	#按照步长生成的一串数字
+    curve_y = [quadratic_function (i, *popt) for i in curve_x]	# 根据x0(按照步长生成的一串数字)来计算y1值
+    plt.plot(curve_x, curve_y, color='blue', label='Fitted Curve')   	#绘制拟合曲线
+    plt.legend()
+    plt.show()    #显示函数图像
+
+if __name__ == '__main__':
+    curve_data = [[-375,250],[-750,0],[-1000,-500],[0,0],[375,-250],[750,0],[1000,500]]
+    x = np.array([point[0] for point in curve_data]) # 为二次函数.txt
+    y = np.array([point[1] for point in curve_data])
+    draw_line(-1000, 1000, x, y)
+
+# 下面是一个用于拟合曲线的最小二乘法的Python代码示例：
+
+# import numpy as np
+# import matplotlib.pyplot as plt
+#
+# # 定义x和y坐标数据
+# x = np.array([1, 2, 3, 4, 5])
+# y = np.array([2, 3, 4, 5, 6])
+#
+# # 定义多项式阶数m
+# m = 2
+#
+# # 构造A矩阵
+# A = np.vander(x, m + 1, increasing=True)
+#
+# # 计算拟合系数theta
+# theta = np.linalg.lstsq(A, y, rcond=None)[0]
+#
+# # 使用theta和x的幂次计算拟合曲线
+# x_fit = np.linspace(x.min(), x.max(), 100)
+# y_fit = np.polyval(theta[::-1], x_fit)
+#
+# # 创建图形对象并绘制拟合曲线和样本点
+# fig, ax = plt.subplots()
+# ax.plot(x_fit, y_fit, label='Fitted curve')
+# ax.scatter(x, y, label='Data points')
+#
+# # 添加标签
+# ax.set_xlabel('x')
+# ax.set_ylabel('y')
+# ax.set_title('Curve fitting using Least Squares')
+#
+# # 显示图形
+# plt.legend()
+# plt.show()

X3.py

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+# -*- coding: utf-8 -*-
+# Time : 2023/8/9 10:20
+# Author : lirunsheng
+# User : l'r's
+# Software: PyCharm
+# File : X3.py
+
+import mpl_toolkits.axisartist as axisartist
+from scipy.optimize import curve_fit
+from pandas import DataFrame
+import matplotlib.pyplot as plt
+import numpy as np
+import pylab as mpl
+from tkinter import *
+import data as gl_data
+import pandas as pd
+import tkinter
+import sys
+import tkinter as tk
+from tkinter import filedialog
+
+mpl.rcParams['font.sans-serif'] = ['SimHei']  		# 解决matplotlib中文不显示问题
+plt.rcParams['axes.unicode_minus'] = False # 解决matplotlib负数坐标显示问题
+
+# 创建一个二维数组sampleData，用于存储样本数据
+sampleData = []
+
+def askfile():# 从本地选择一个文件，并返回文件的路径
+    global sampleData
+    # 弹出文件选择对话框，选择要打开的文本文件
+    file_path = filedialog.askopenfilename(filetypes=[('Text Files', '*.txt')])
+
+    # 如果没有选择文件，直接返回
+    if not file_path:
+        return
+    # 步骤1：打开样本数据集文件并读取每行数据
+    with open(file_path, 'r') as file:
+        lines = file.readlines()
+
+    # 步骤2：遍历所有行，将每行数据解析为sx和sy值，转换为浮点数并存储到sampleData中
+    for line in lines:
+        sx, sy = line.strip().split(' ')
+        sx = float(sx)
+        sy = float(sy)
+        sampleData.append([sx, sy])
+
+    # # 步骤3：使用循环遍历样本数据并打印出来
+    # for data in sampleData:
+    #     print(data)
+# if __name__ == '__main__':
+#     askfile()
+def draw_axis(low, high, step=250):
+    fig = plt.figure(figsize=(4.4, 3.2)) # 设置显示大小
+    ax = axisartist.Subplot(fig, 111)	# 使用axisartist.Subplot方法创建一个绘图区对象ax
+    fig.add_axes(ax)   # 将绘图区对象添加到画布中
+    ax.axis[:].set_visible(False)# 通过set_visible方法设置绘图区所有坐标轴隐藏
+    ax.axis["x"] = ax.new_floating_axis(0, 0)	# 添加新的x坐标轴
+    ax.axis["x"].set_axisline_style("-|>", size=1.0) # 给x坐标轴加上箭头
+    ax.axis["y"] = ax.new_floating_axis(1, 0)	# 添加新的y坐标轴
+    ax.axis["y"].set_axisline_style("-|>", size=1.0) # y坐标轴加上箭头
+    ax.axis["x"].set_axis_direction("bottom")	# 设置x、y轴上刻度显示方向
+    ax.axis["y"].set_axis_direction("left")	# 设置x、y轴上刻度显示方向
+    plt.xlim(low, high)  # 把x轴的刻度范围设置
+    plt.ylim(low, high)  # 把y轴的刻度范围设置
+    ax.set_xticks(np.arange(low, high + 5, step))  # 把x轴的刻度间隔设置
+    ax.set_yticks(np.arange(low, high + 5, step))  # 把y轴的刻度间隔设置
+
+def generate_and_plot_sample_data(low, high):
+    num_samples = 25		#设置样本点数量
+    gl_data.X = np.random.randint(low=low, high=high, size=num_samples)#随机生成x值
+    print(gl_data.X)
+    gl_data.Y = np.random.randint(low=low, high=high, size=num_samples)#随机生成y值
+    # 提取样本数据的x坐标和y坐标
+    # x_values = [point[0] for point in sampleData]
+    # print(x_values)
+    # y_values = [point[1] for point in sampleData]
+    draw_axis(low, high)	#绘制坐标轴
+    plt.scatter(gl_data.X,gl_data.Y, color='red')  # 绘制样本数据点
+    plt.savefig(r"dot2.png", facecolor='w')	# 保存到本地
+    plt.close()	# 清除内存
+    # set_phtot(1)	#显示到主界面
+# if __name__ == '__main__':
+#     askfile()
+#     # generate_and_plot_sample_data(gl_data.LOW, gl_data.HIGH)
+def quadratic_function(x, a, b, c):#构造二次函数y = a * X^2 + b * X + C
+    return a * x ** 2 + b * x + c
+def draw_dots_and_line(low, high, sx, sy):
+    draw_axis(low, high)
+    popt, pcov = curve_fit(quadratic_function, sx, sy)# 用curve_fit来对点进行拟合
+    positive_mask = sy >= 0.0#给样本点分类
+    negative_mask = sy < 0.0#给样本点分类
+    positive_colors = ['red' if x >= 0.0 else 'blue' for x in sx]#给样本点分类
+    negative_colors = ['green' if x >= 0.0 else 'purple' for x in sx]#给样本点分类
+    #根据样本点类型决定样本点颜色
+    plt.scatter(gl_data.X[positive_mask], gl_data.Y[positive_mask], color=np.array(positive_colors)[positive_mask], lw=1)
+    plt.scatter(gl_data.X[negative_mask], gl_data.Y[negative_mask], color=np.array(negative_colors)[negative_mask], lw=1)
+    curve_x = np.arange(low, high)#按照步长生成的一串数字
+    curve_y = [quadratic_function (i, * popt) for i in curve_x]# 根据x来计算y1值
+    plt.plot(curve_x, curve_y, color='blue', label='Fitted Curve')#绘制拟合曲线
+    plt.savefig(r"dot5.png", facecolor='w')  # 保存到本地
+    plt.legend()
+    plt.show()
+    return popt
+# if __name__ == '__main__':
+#     askfile()
+#     gl_data.x = np.array([point[0] for point in sampleData]) # 为二次函数.txt
+#     gl_data.y = np.array([point[1] for point in sampleData])
+#     popt = draw_dots_and_line(gl_data.low, gl_data.high, gl_data.x, gl_data.y)
+#     a,b,c = popt
+#     print(a,b,c)
+
+def input_num(root_tk):
+    global top
+    top = tk.Toplevel(root_tk)
+    top.geometry("300x50")
+    top.title('坐标点个数')
+    label1 = Label(top, text="坐标点个数")
+    label1.grid(row=0)  # 这里的side可以赋值为LEFT  RTGHT TOP  BOTTOM
+    num1 = IntVar()
+    entry1 = Entry(top, textvariable=num1)
+    num1.set(0)
+    entry1.grid(row=0, column=1)
+    Label(top, text=" ").grid(row=0, column=3)
+    Button(top, text="确定", command=lambda: input_data(root_tk, int(entry1.get()))).grid(row=0, column=3)
+    top.mainloop()
+
+def add_sample_data():
+    global sample_x, sample_y, sample_data
+    global entry_x,entry_y,label_status, numx
+    try:
+        x = float(entry_x.get())
+        y = float(entry_y.get())
+    except:
+        label_status.config(text="输入不合法")
+        return
+    entry_x.delete(0, tk.END)
+    entry_y.delete(0, tk.END)
+    if min(x, y) < gl_data.LOW or max(x, y) > gl_data.HIGH:
+        label_status.config(text="输入超过范围")
+        return
+    elif len(sample_data) < numx:
+        label_status.config(text="点对已添加")
+        sample_data.append((x, y))
+        sample_x.append(x)
+        sample_y.append(y)
+    else:
+        label_status.config(text="已达到最大数量")
+def check_sample_data():
+    global label_status,numx,sample_x,sample_y,sample_data
+    if len(sample_data) == numx:
+        label_status.config(text="已达到最大数量")
+        gl_data.X = np.array(sample_x)
+        gl_data.Y = np.array(sample_y)
+        print('已添加', sample_data)
+        sys.exit()
+    else:
+        label_status.config(text="还需输入{}个点对".format(numx - len(sample_data)))
+        print(sample_data)
+
+def input_data(root_tk, num):
+    global top
+    global sample_x,sample_y,sample_data
+    global numx
+    numx = num
+    sample_x = []
+    sample_y = []
+    sample_data = []
+    top.destroy()
+    top = tk.Toplevel(root_tk)
+    top.geometry("300x200")
+    top.title('坐标')
+    global entry_x, entry_y, label_status
+    label_x = tk.Label(top, text="X 值：")
+    label_x.pack()
+    entry_x = tk.Entry(top)
+    entry_x.pack()
+    label_y = tk.Label(top, text="Y 值：")
+    label_y.pack()
+    entry_y = tk.Entry(top)
+    entry_y.pack()
+    button_add = tk.Button(top, text="添加", command=add_sample_data)
+    button_add.pack()
+    button_check = tk.Button(top, text="检查", command=check_sample_data)
+    button_check.pack()
+    label_status = tk.Label(top, text="")
+    label_status.pack()
+    top.mainloop()
+
+# if __name__ == '__main__':
+#     root = tk.Tk()
+#     root.withdraw()
+#     input_num(root)
+
+# 定义误差函数
+def error_func(x_data, y_data, a, b, c):
+    y_pred = exponential_function(x_data, a, b, c)
+    error = np.sum((y_data - y_pred) ** 2)
+    residual = y_data - y_pred
+    ss_res = np.sum(residual ** 2)
+    ss_tot = np.sum((y_data - np.mean(y_data)) ** 2)
+    r_squared = 1 - (ss_res / ss_tot)
+    return error,r_squared
+
+# 给出一个二次函数拟合的例子，读者可自己写拟合函数
+def exponential_function(x, a, b, c):
+    return a * x ** 2 + b * x + c
+
+def fit(sample_data): # 随机生成样本数据
+    x_data = np.array([data[0] for data in sample_data])
+    y_data = np.array([data[1] for data in sample_data]) # 拟合样本数据
+    popt, pcov = curve_fit(exponential_function, x_data, y_data) # 计算拟合结果
+    # 计算拟合误差
+    error,r_squared = error_func(x_data, y_data, *popt)
+    fit_function_name = exponential_function.__name__# 打印拟合函数的形式、系数、误差和优度
+    print("拟合函数形式：{}".format(fit_function_name))
+    print("拟合系数：{}".format(popt))
+    print("误差：{:.4f}".format(error))
+    print("拟合优度（R^2）：{:.4f}".format(r_squared))
+# if __name__ == '__main__':
+#     askfile()
+#     fit(sampleData) # 对当前x、y值进行拟合
+# # 给出一个指数函数拟合的例子，读者可自己写拟合函数
+# def fit_function(x,a,b,c):
+#     return a * np.exp(b * x) + c
+#
+# def fit(sample_data): # 随机生成样本数据
+#     x_data = np.array([data[0] for data in sample_data])
+#     y_data = np.array([data[1] for data in sample_data]) # 拟合样本数据
+#     popt, pcov = curve_fit(fit_function, x_data, y_data) # 计算拟合结果
+#     y_fit = fit_function(x_data, *popt)
+#     residuals = y_data - y_fit
+#     ss_res = np.sum(residuals**2)
+#     ss_tot = np.sum((y_data - np.mean(y_data))**2)
+#     r_squared = 1 - (ss_res / ss_tot)
+#     fit_function_name = fit_function.__name__# 打印拟合函数的形式、系数、误差和优度
+#     print("拟合函数形式：{}".format(fit_function_name))
+#     print("拟合系数：{}".format(popt))
+#     print("误差：{:.4f}".format(np.sqrt(np.mean(residuals**2))))
+#     print("拟合优度（R^2）：{:.4f}".format(r_squared))
+# if __name__ == '__main__':
+#     askfile()
+#     fit(sampleData) # 对当前x、y值进行拟合
+
+def change_Q(no):
+    gl_data.Quadrant = no 	#更改全局变量的象限显示
+    if no:		#若为一象限，则修改显示下限为0
+        gl_data.LOW = 0
+    else:		#若为四象限，则修改显示下限为-gl_data.MAXV
+        gl_data.LOW = -gl_data.MAXV
+    q_button()	#更新象限显示面板
+
+def q_button():
+    r = 7.5
+    rr = 2.5
+    for widget in q_root.winfo_children():
+        widget.destroy()
+    q_cv = tk.Canvas(q_root, width=450, height=500)
+    q_cv.place(x=0, y=0)
+    l = tk.Label(q_root, text='坐标轴', bd=0, font=("微软雅黑", 16) , anchor=W)
+    l.place(x=20, y=0, width=80, height=50,)
+    # 四象b限按钮
+    b1 = tk.Button(q_root, text='四象限', bd=0,  font=("微软雅黑", 16)
+                               , command=lambda: change_Q(0), anchor=W)
+    b1.place(x=170, y=0, width=80, height=50,)
+    # 一象限按钮
+    b2 = tk.Button(q_root, text='一象限', bd=0, font=("微软雅黑", 16)
+                   , command=lambda: change_Q(1), anchor=W)
+    b2.place(x=320, y=0, width=80, height=50,)
+    # 绘制标记框
+    q_cv.create_oval(140 - r, 25 - r, 140 + r, 25 + r, fill="white", width=1, outline="black")
+    q_cv.create_oval(290 - r, 25 - r, 290 + r, 25 + r , fill="white", width=1, outline="black")
+    # 根据当前的象限选择值来填充标记框
+    if gl_data.Quadrant == 0:
+        q_cv.create_oval(140 - rr, 25 - rr, 140 + rr, 25 + rr, fill="black", width=1, outline="black")# 绘制象限
+        # Q_cv.create_rectangle(80, 80, 270, 270, fill="white")  # 第一象限
+        # Q_cv.create_rectangle(270, 80, 500, 270, fill="red")  # 第二象限
+        # Q_cv.create_rectangle(80, 270, 270, 480, fill="blue")  # 第三象限
+        # Q_cv.create_rectangle(270, 270, 500, 480, fill="green")  # 第四象限
+    else:
+        q_cv.create_oval(290 - rr, 25 - rr, 290 + rr, 25 + rr, fill="black", width=1, outline="black")
+# if __name__ == '__main__':
+#     # 象限选择相关界面
+#     q_root = tk.Tk()
+#     q_root.geometry("500x550")  # 设置窗口的大小和位置
+#     q_button()
+#     q_root.mainloop()
+
+# 定义模型为y=ax+b
+def model(x, a, b):
+    return a*x + b
+
+# 定义误差函数error_function()
+def error_function(x,y,a, b):
+    y_pred = model(x, a, b)
+    error = np.mean((y - y_pred)**2)
+    return error
+
+# 定义梯度函数gradient()
+def gradient(a, b,x,y):
+    y_pred = model(x, a, b)
+    gradient_a = 2*np.mean((y_pred - y)*x)
+    gradient_b = 2*np.mean(y_pred - y)
+    return gradient_a, gradient_b
+
+if __name__ == '__main__':
+    # 读取sampledata值
+    sampledata = [0, 1, 2, 3, 4, 5, 6, 7, 8, 9]
+    x = np.array(sampledata)
+    y = np.array([-2, 1, 0, 1, 2, 3, 4, 5, 6, 8])
+    # 初始化参数
+    a = 0
+    b = 0
+    learning_rate = 0.01
+    num_iterations = 1000
+    # 梯度下降算法
+    for i in range(num_iterations):
+        grad_a, grad_b = gradient(a, b,x,y)
+        a -= learning_rate * grad_a
+        b -= learning_rate * grad_b
+    # 输出最终拟合结果
+    final_error = error_function(x,y,a, b)
+    # gl_data.X = x  # 为二次函数.txt
+    # gl_data.Y = y
+    # draw_axis(-100, 100)
+    # positive_mask = x >= 0.0  # 给样本点分类
+    # negative_mask = y < 0.0  # 给样本点分类
+    # positive_colors = ['red' if x >= 0.0 else 'blue' for x in x]  # 给样本点分类
+    # negative_colors = ['green' if x >= 0.0 else 'purple' for x in x]  # 给样本点分类
+    # # 根据样本点类型决定样本点颜色
+    # plt.scatter(gl_data.X[positive_mask], gl_data.Y[positive_mask], color=np.array(positive_colors)[positive_mask],
+    #             lw=1)
+    # plt.scatter(gl_data.X[negative_mask], gl_data.Y[negative_mask], color=np.array(negative_colors)[negative_mask],
+    #             lw=1)
+    # curve_x = np.arange(-1000, 1000)  # 按照步长生成的一串数字
+    # curve_y = [model(i, a, b) for i in curve_x]  # 根据x来计算y1值
+    # plt.plot(curve_x, curve_y, color='blue', label='Fitted Curve')  # 绘制拟合曲线
+    # plt.legend()
+    # plt.show()
+    print("拟合函数形式: y = ax + b")
+    print("系数 a:{:.2f}".format(a))
+    print("系数 b:{:.2f}".format( b))
+    print("误差计算方法: 均方误差")
+    print("最终误差:{:.2f}".format(final_error))

X4.py

@@ -0,0 +1,225 @@
+# -*- coding: utf-8 -*-
+# Time : 2023/8/9 10:20
+# Author : lirunsheng
+# User : l'r's
+# Software: PyCharm
+# File : X4.py
+
+# -*- encoding: utf-8 -*-
+"""
+ @Author: packy945
+ @FileName: main.py
+ @DateTime: 2023/5/30 15:29
+ @SoftWare: PyCharm
+"""
+import sys
+
+from fitting import *
+import numpy as np
+import data as gl_data
+import input
+import tkinter as tk
+from tkinter import *
+import tkinter.filedialog  # 注意次数要将文件对话框导入
+
+global Q_root,F_root
+global root_window
+global label1,label2,label3
+
+def window():
+    global root_window
+    global label1, label2, label3
+    root_window = Tk()
+    root_window.title('函数拟合')
+    root_window.geometry('900x600')  # 设置窗口大小:宽x高,注,此处不能为 "*",必须使用 "x"
+    # 设置主窗口的背景颜色,颜色值可以是英文单词，或者颜色值的16进制数,除此之外还可以使用Tk内置的颜色常量
+    root_window["background"] = "white"
+    root_window.resizable(0, 0)  # 防止用户调整尺寸
+    label1 = tk.Label(root_window, text="样本数据\n集文件", font=('Times', 8), bg="white",
+                      width=13, height=3,  # 设置标签内容区大小
+                      padx=0, pady=0, borderwidth=0, )
+    label1.place(x=10, y=4)  # 设置填充区距离、边框宽度和其样式（凹陷式）
+    label3 = tk.Label(root_window, text="", font=('Times', 8), bg="white", fg="black",
+                      width=39, height=2, padx=0, pady=0, borderwidth=0, relief="ridge", highlightcolor="blue")
+    label3.place(x=122, y=10)
+    # 使用按钮控件调用函数
+    tk.Button(root_window, text="装载", relief=RAISED, command=lambda: askfile()).place(x=370, y=12)
+    label2 = tk.Label(root_window, text="拟合曲线类型", font=('Times', 12), bg="white",
+                      width=20, height=3, # 设置标签内容区大小
+                      padx=0, pady=0, borderwidth=0, )
+    # 设置填充区距离、边框宽度和其样式（凹陷式）
+    label2.place(x=450, y=4)
+    gl_data.Canvas2 = tk.Canvas(root_window, bg='white', width=450, height=330)
+    gl_data.Canvas2.place(x=4, y=60)
+# 定义一个处理文件的相关函数
+def askfile():
+    # 从本地选择一个文件，并返回文件的路径
+    filename = tkinter.filedialog.askopenfilename()
+    if filename != '':#若选中了一个文件，则对文件进行读取
+        label3.config(text=filename)#显示文件路径
+        read_sample_data(filename)#将文件读取并存到sampleData中
+        # print_sample_data(filename)#将文件读取并逐行输出
+        selfdata_show(gl_data.X, gl_data.Y, gl_data.LOW, gl_data.HIGH)
+    else:#若未选择文件，则显示为空
+        label3.config(text='')
+
+def print_sample_data(file_path):#打开对应文件
+    with open(file_path, 'r') as file:
+        for line in file:#逐行读取文件
+            line = line.strip('\n')#移除换行符
+            sx, sy = line.split(' ')#以空格分割x，y
+            print(f'sx: {float(sx)}, sy: {float(sy)}')#将sx、sy转换为浮点数并打印
+
+
+def read_sample_data(file_path):
+    x, y = [], []#初始化x，y
+    with open(file_path, 'r') as file:
+        for line in file:#逐行读文件
+            line = line.strip('\n')#移除换行符
+            sx, sy = line.split(' ')#以空格分割x，y
+            x.append(float(sx))#将sx转换为浮点数并加入数组
+            y.append(float(sy))#将sy转换为浮点数并加入数组
+    gl_data.X, gl_data.Y = np.array(x), np.array(y)#x，y数组转为array并赋值给全局变量
+
+def buttons():
+    # 随机生成样本点并显示
+    b_dot = tk.Button(root_window, text="生成\n数据集", relief=RAISED, bd=4, bg="white", font=("微软雅黑", 10),
+                   command=lambda: generate_and_plot_sample_data(gl_data.LOW, gl_data.HIGH))
+    b_dot.place(x=455, y=410)
+    # 显示当前样本点
+    b_show = tk.Button(root_window, text="显示\n数据集", relief=RAISED, bd=4, bg="white", font=("微软雅黑", 10),
+              command=lambda: selfdata_show(gl_data.X, gl_data.Y, gl_data.LOW, gl_data.HIGH))
+    b_show.place(x=510, y=410)
+    # 显示数据集与曲线
+    b_line = tk.Button(root_window, text="显示数据\n集与曲线", relief=RAISED, bd=4, bg="white", font=("微软雅黑", 10),
+                   command=lambda: draw_dots_and_line(gl_data.Xian_index, gl_data.LOW, gl_data.HIGH, gl_data.X, gl_data.Y))
+    b_line.place(x=565, y=410)
+    # 手动输入数据集
+    b_input = tk.Button(root_window, text="手动输入数据集", relief=RAISED, bd=4, bg="white", pady=7, font=("微软雅黑", 13),
+                        command=lambda: input.input_num(root_window))
+    b_input.place(x=633, y=410)
+    # 拟合并输出拟合结果
+    b_fit = tk.Button(root_window, text="拟合", relief=RAISED, bd=4, bg="white", pady=7, font=("微软雅黑", 13),
+                   command=lambda: fit_data(gl_data.Xian_index, gl_data.X, gl_data.Y))
+    b_fit.place(x=771, y=410)
+def show_fit():
+    L = tk.Label(root_window, text='结果输出：', bg='white', font=("微软雅黑", 16)
+                                   , anchor=W)
+    L.place(x=20, y=480, width=100, height=30)
+    ans = tk.Label(root_window, text=gl_data.Out, font=("微软雅黑", 14)
+                                   , anchor=W, justify='left')
+    ans.place(x=120, y=480, width=760, height=100)
+    print(gl_data.Out)
+
+def fit_data(xian_index, sx, sy):
+    # gl_data.yvals_pow = []
+    cur = function.Fun[xian_index]  # 装载正在选择的函数
+    func = cur.get_fun()#获取当前函数func
+    popt, pcov = curve_fit(func, sx, sy)# 用curve_fit来对点进行拟合
+    yvals_pow = func(gl_data.X, *popt)
+    rr = gl_data.goodness_of_fit(yvals_pow, gl_data.Y)# 计算本次拟合的R*R值，用于表示拟合优度
+    # 输出拟合后的各个参数值
+    ans = '\n函数系数：'
+    for i in range(cur.variable):
+        if i == 4:
+            ans += '\n'
+        if i != 0:
+            ans += ', '
+        ans += chr(ord('a') + i) + '=' + '{:.2e}'.format(popt[i])  # str(round(gl_data.popt[i], 3))
+    gl_data.Out = '函数形式：' + cur.name + '  '
+    gl_data.Out += cur.demo
+    gl_data.Out += ans
+    gl_data.Out += '\n拟合优度(R\u00b2)：' + str(round(rr, 5))
+    show_fit()# 显示函数信息到输出框
+
+def change_Q(no):
+    gl_data.Quadrant = no #更改全局变量的象限显示
+    if no:#若为一象限，则修改显示下限为0
+        gl_data.LOW = 0
+    else:#若为四象限，则修改显示下限为-gl_data.maxV
+        gl_data.LOW = -gl_data.MAXV
+    q_button()#更新象限显示面板
+
+def q_button():
+    r = 7.5
+    rr = 2.5
+    for widget in Q_root.winfo_children():
+        widget.destroy()
+    q_cv = tk.Canvas(Q_root, width=400, height=50)
+    q_cv.place(x=0, y=0)
+    l = tk.Label(Q_root, text='坐标轴', bd=0, font=("微软雅黑", 16)
+                               , anchor=W)
+    l.place(x=20, y=0, width=80, height=50,)
+    # 四象限按钮
+    b1 = tk.Button(Q_root, text='四象限', bd=0,  font=("微软雅黑", 16)
+                               , command=lambda: change_Q(0), anchor=W)
+    b1.place(x=170, y=0, width=80, height=50,)
+    # 一象限按钮
+    b2 = tk.Button(Q_root, text='一象限', bd=0, font=("微软雅黑", 16)
+                   , command=lambda: change_Q(1), anchor=W)
+    b2.place(x=320, y=0, width=80, height=50,)
+    # 绘制标记框
+    q_cv.create_oval(140 - r, 25 - r, 140 + r, 25 + r
+                     , fill="white", width=1, outline="black")
+    q_cv.create_oval(290 - r, 25 - r, 290 + r, 25 + r
+                     , fill="white", width=1, outline="black")
+    # 根据当前的象限选择值来填充标记框
+    if gl_data.Quadrant == 0:
+        q_cv.create_oval(140 - rr, 25 - rr, 140 + rr, 25 + rr
+                     , fill="black", width=1, outline="black")
+    else:
+        q_cv.create_oval(290 - rr, 25 - rr, 290 + rr, 25 + rr
+                     , fill="black", width=1, outline="black")
+
+
+def change_f(no):
+    gl_data.Xian_index = no#设置全局函数编号为该函数
+    f_button()#重新绘制函数显示界面
+
+def f_button():
+    r = 7.5#设置按钮大小
+    rr = 2.5#设置按钮大小
+    for widget in F_root.winfo_children():
+        widget.destroy()#清空原有按钮
+    f_cv = tk.Canvas(F_root, width=400, height=330)#新建画布
+    f_cv.place(x=0, y=0)#放置画布
+    f_cv.create_rectangle(2, 2, 398, 328, fill='white', outline="#0099ff")#设置画布边框及底色
+    cur = 0#函数计数
+
+    for fun in function.Fit_type_library:#遍历函数库
+        f = function.Fit_type_library.get(fun)#获取函数具体信息
+        if function.Show[f[0]] == 1:# 如果show为1则显示
+            f_cv.create_oval(20 - r, 20 + 15 + cur * 30 - r, 20 + r, 20 + 15 + cur * 30 + r
+                             , fill="white", width=1, outline="black")# 绘制标记框
+            if f[0] == gl_data.Xian_index:# 若选择为当前函数则标记
+                f_cv.create_oval(20 - rr, 20 + 15 + cur * 30 - rr, 20 + rr, 20 + 15 + cur * 30 + rr
+                                 , fill="black", width=1, outline="black")
+            # 绘制切换按钮,单击则将当前使用函数切换为该函数
+            button = tk.Button(F_root, text=f[2] + ' ' + f[1], bd=0, bg="white", font=("微软雅黑", 12)
+                               , command=lambda x=f[0]: change_f(x), anchor=W)
+            button.place(x=40, y=20 + cur * 30, width=300, height=30)
+            cur += 1#计数加一
+
+def close_window():
+    sys.exit()
+def main():
+    global Q_root, F_root,root_window
+    gl_data.X = []
+    gl_data.X = []
+    window()
+    function.f_read()
+    # 函数选择相关界面
+    F_root = tk.Frame(root_window, width=400, height=330, bg='white', )
+    F_root.place(x=490, y=60)
+    # 象限选择相关界面
+    Q_root = tk.Frame(root_window, width=400, height=50, bg='white', )
+    Q_root.place(x=20, y=410)
+    buttons()
+    f_button()
+    q_button()
+    show_fit()
+    root_window.protocol("WM_DELETE_WINDOW", close_window)
+    root_window.mainloop()
+if __name__ == '__main__':
+    main()
+    pass

X5.py

@@ -0,0 +1,265 @@
+# -*- coding: utf-8 -*-
+# Time : 2023/8/9 10:20
+# Author : lirunsheng
+# User : l'r's
+# Software: PyCharm
+# File : X4.py
+
+# -*- encoding: utf-8 -*-
+"""
+ @Author: packy945
+ @FileName: main.py
+ @DateTime: 2023/5/30 15:29
+ @SoftWare: PyCharm
+"""
+import sys
+from fitting import *
+import numpy as np
+import data as gl_data
+import input
+import tkinter as tk
+from tkinter import *
+import tkinter.filedialog  # 注意次数要将文件对话框导入
+# from demo1 import Addfunc
+
+global Q_root,F_root
+global root_window
+global label1,label2,label3
+
+class Addfunc():
+    def __init__(self):
+        self.r = 7.5 # 设置按钮大小
+        self.rr = 2.5# 设置按钮大小
+        self.window = tk.Tk() # 新建函数增加窗口
+        self.window.title("新增函数曲线")#设置窗口标题
+        self.window.geometry('400x300')#设置窗口大小
+        self.show()#显示按钮
+        self.window.mainloop()#运行UI界面
+
+    def show(self):
+        for widget in self.window.winfo_children():
+            widget.destroy()#清空已有组件
+        self.add_cv = tk.Canvas(self.window, width=400, height=300)  # 新建画布
+        self.add_cv.place(x=0, y=0)  # 放置画布
+        cur = 0#记录已有按钮个数
+        for f in function.Fun:#遍历已有函数
+            self.add_cv.create_oval(20 - self.r, 20 + 15 + cur * 30 - self.r, 20 + self.r, 20 + 15 + cur * 30 + self.r
+                               , fill="white", width=1, outline="black")# 绘制圆圈
+            if f.show == 1:#若为当前选中函数，则标记
+                self.add_cv.create_oval(20 - self.rr, 20 + 15 + cur * 30 - self.rr, 20 + self.rr, 20 + 15 + cur * 30 + self.rr
+                                   , fill="black", width=1, outline="black")
+            button = tk.Button(self.window, text=f.name + f.demo, bd=0, font=("微软雅黑", 12)
+                               , command=lambda x=f.no: self.change(x), anchor=W)#设置选择按钮
+            button.place(x=40, y=20 + cur * 30, width=300, height=30)#放置选择按钮
+            cur += 1#计数加一
+
+    def change(self, no):#切换函数显示情况
+        function.Show[no] = not function.Show[no]
+        function.Fun[no].show = not function.Fun[no].show
+        self.show()#更新函数选择面板
+        f_button()#更新函数显示界面
+# class AddFunc(Addfunc):
+#     def change(self, no):
+#         # super().change(no)
+#         function.Show[no] = not function.Show[no]
+#         function.Fun[no].show = not function.Fun[no].show
+#         self.show()  # 更新函数选择面板
+#         f_button()
+
+def addfunc():
+    Addfunc()
+    # AddFunc()
+def window():
+    global root_window
+    global label1, label2, label3
+    root_window = Tk()
+    root_window.title('函数拟合')
+    root_window.geometry('900x600')  # 设置窗口大小:宽x高,注,此处不能为 "*",必须使用 "x"
+    # 设置主窗口的背景颜色,颜色值可以是英文单词，或者颜色值的16进制数,除此之外还可以使用Tk内置的颜色常量
+    root_window["background"] = "white"
+    root_window.resizable(0, 0)  # 防止用户调整尺寸
+    label1 = tk.Label(root_window, text="样本数据\n集文件", font=('Times', 8), bg="white",
+                      width=13, height=3,  # 设置标签内容区大小
+                      padx=0, pady=0, borderwidth=0, )
+    label1.place(x=10, y=4)  # 设置填充区距离、边框宽度和其样式（凹陷式）
+    label3 = tk.Label(root_window, text="", font=('Times', 8), bg="white", fg="black",
+                      width=39, height=2, padx=0, pady=0, borderwidth=0, relief="ridge", highlightcolor="blue")
+    label3.place(x=122, y=10)
+    # 使用按钮控件调用函数
+    tk.Button(root_window, text="装载", relief=RAISED, command=lambda: askfile()).place(x=370, y=12)
+    label2 = tk.Label(root_window, text="拟合曲线类型", font=('Times', 12), bg="white",
+                      width=20, height=3, # 设置标签内容区大小
+                      padx=0, pady=0, borderwidth=0, )
+    # 设置填充区距离、边框宽度和其样式（凹陷式）
+    label2.place(x=450, y=4)
+    gl_data.Canvas2 = tk.Canvas(root_window, bg='white', width=450, height=330)
+    gl_data.Canvas2.place(x=4, y=60)
+# 定义一个处理文件的相关函数
+def askfile():
+    # 从本地选择一个文件，并返回文件的路径
+    filename = tkinter.filedialog.askopenfilename()
+    if filename != '':#若选中了一个文件，则对文件进行读取
+        label3.config(text=filename)#显示文件路径
+        read_sample_data(filename)#将文件读取并存到sampleData中
+        # print_sample_data(filename)#将文件读取并逐行输出
+        selfdata_show(gl_data.X, gl_data.Y, gl_data.LOW, gl_data.HIGH)
+    else:#若未选择文件，则显示为空
+        label3.config(text='')
+
+def print_sample_data(file_path):#打开对应文件
+    with open(file_path, 'r') as file:
+        for line in file:#逐行读取文件
+            line = line.strip('\n')#移除换行符
+            sx, sy = line.split(' ')#以空格分割x，y
+            print(f'sx: {float(sx)}, sy: {float(sy)}')#将sx、sy转换为浮点数并打印
+
+def read_sample_data(file_path):
+    x, y = [], []#初始化x，y
+    with open(file_path, 'r') as file:
+        for line in file:#逐行读文件
+            line = line.strip('\n')#移除换行符
+            sx, sy = line.split(' ')#以空格分割x，y
+            x.append(float(sx))#将sx转换为浮点数并加入数组
+            y.append(float(sy))#将sy转换为浮点数并加入数组
+    gl_data.X, gl_data.Y = np.array(x), np.array(y)#x，y数组转为array并赋值给全局变量
+
+def buttons():
+    # 随机生成样本点并显示
+    b_dot = tk.Button(root_window, text="生成\n数据集", relief=RAISED, bd=4, bg="white", font=("微软雅黑", 10),
+                   command=lambda: generate_and_plot_sample_data(gl_data.LOW, gl_data.HIGH))
+    b_dot.place(x=455, y=410)
+    # 显示当前样本点
+    b_show = tk.Button(root_window, text="显示\n数据集", relief=RAISED, bd=4, bg="white", font=("微软雅黑", 10),
+              command=lambda: selfdata_show(gl_data.X, gl_data.Y, gl_data.LOW, gl_data.HIGH))
+    b_show.place(x=510, y=410)
+    # 显示数据集与曲线
+    b_line = tk.Button(root_window, text="显示数据\n集与曲线", relief=RAISED, bd=4, bg="white", font=("微软雅黑", 10),
+                   command=lambda: draw_dots_and_line(gl_data.Xian_index, gl_data.LOW, gl_data.HIGH, gl_data.X, gl_data.Y))
+    b_line.place(x=565, y=410)
+    # 手动输入数据集
+    b_input = tk.Button(root_window, text="手动输入数据集", relief=RAISED, bd=4, bg="white", pady=7, font=("微软雅黑", 13),
+                        command=lambda: input.input_num(root_window))
+    b_input.place(x=633, y=410)
+    # 拟合并输出拟合结果
+    b_fit = tk.Button(root_window, text="拟合", relief=RAISED, bd=4, bg="white", pady=7, font=("微软雅黑", 13),
+                   command=lambda: fit_data(gl_data.Xian_index, gl_data.X, gl_data.Y))
+    b_fit.place(x=771, y=410)
+def show_fit():
+    L = tk.Label(root_window, text='结果输出：', bg='white', font=("微软雅黑", 16)
+                                   , anchor=W)
+    L.place(x=20, y=480, width=100, height=30)
+    sout = str(gl_data.Out)
+    ans = tk.Label(root_window, text=sout, font=("微软雅黑", 14)
+                                   , anchor=W, justify='left')
+    ans.place(x=120, y=480, width=760, height=100)
+    print(sout)
+def fit_data(xian_index, sx, sy):
+    # gl_data.yvals_pow = []
+    cur = function.Fun[xian_index]  # 装载正在选择的函数
+    func = cur.get_fun()#获取当前函数func
+    popt, pcov = curve_fit(func, sx, sy)# 用curve_fit来对点进行拟合
+    yvals_pow = func(gl_data.X, *popt)
+    rr = gl_data.goodness_of_fit(yvals_pow, gl_data.Y)# 计算本次拟合的R*R值，用于表示拟合优度
+    # 输出拟合后的各个参数值
+    ans = '\n函数系数：'
+    for i in range(cur.variable):
+        if i == 4:
+            ans += '\n'
+        if i != 0:
+            ans += ', '
+        ans += chr(ord('a') + i) + '=' + '{:.2e}'.format(popt[i])  # str(round(gl_data.popt[i], 3))
+    gl_data.Out = '函数形式：' + cur.name + '  '
+    gl_data.Out += cur.demo
+    gl_data.Out += ans
+    gl_data.Out += '\n拟合优度(R\u00b2)：' + str(round(rr, 5))
+    show_fit()# 显示函数信息到输出框
+
+def change_Q(no):
+    gl_data.Quadrant = no #更改全局变量的象限显示
+    if no:#若为一象限，则修改显示下限为0
+        gl_data.LOW = 0
+    else:#若为四象限，则修改显示下限为-gl_data.maxV
+        gl_data.LOW = -gl_data.MAXV
+    q_button()#更新象限显示面板
+
+def q_button():
+    r = 7.5
+    rr = 2.5
+    for widget in Q_root.winfo_children():
+        widget.destroy()
+    q_cv = tk.Canvas(Q_root, width=400, height=50)
+    q_cv.place(x=0, y=0)
+    l = tk.Label(Q_root, text='坐标轴', bd=0, font=("微软雅黑", 16)
+                               , anchor=W)
+    l.place(x=20, y=0, width=80, height=50,)
+    # 四象限按钮
+    b1 = tk.Button(Q_root, text='四象限', bd=0,  font=("微软雅黑", 16)
+                               , command=lambda: change_Q(0), anchor=W)
+    b1.place(x=170, y=0, width=80, height=50,)
+    # 一象限按钮
+    b2 = tk.Button(Q_root, text='一象限', bd=0, font=("微软雅黑", 16)
+                   , command=lambda: change_Q(1), anchor=W)
+    b2.place(x=320, y=0, width=80, height=50,)
+    # 绘制标记框
+    q_cv.create_oval(140 - r, 25 - r, 140 + r, 25 + r
+                     , fill="white", width=1, outline="black")
+    q_cv.create_oval(290 - r, 25 - r, 290 + r, 25 + r
+                     , fill="white", width=1, outline="black")
+    # 根据当前的象限选择值来填充标记框
+    if gl_data.Quadrant == 0:
+        q_cv.create_oval(140 - rr, 25 - rr, 140 + rr, 25 + rr
+                     , fill="black", width=1, outline="black")
+    else:
+        q_cv.create_oval(290 - rr, 25 - rr, 290 + rr, 25 + rr
+                     , fill="black", width=1, outline="black")
+def change_f(no):
+    gl_data.Xian_index = no#设置全局函数编号为该函数
+    f_button()#重新绘制函数显示界面
+
+def f_button():
+    r = 7.5#设置按钮大小
+    rr = 2.5#设置按钮大小
+    for widget in F_root.winfo_children():
+        widget.destroy()#清空原有按钮
+    f_cv = tk.Canvas(F_root, width=400, height=330)#新建画布
+    f_cv.place(x=0, y=0)#放置画布
+    f_cv.create_rectangle(2, 2, 398, 328, fill='white', outline="#0099ff")#设置画布边框及底色
+    cur = 0#函数计数
+    for fun in function.Fit_type_library:#遍历函数库
+        f = function.Fit_type_library.get(fun)#获取函数具体信息
+        if function.Show[f[0]] == 1:# 如果show为1则显示
+            f_cv.create_oval(20 - r, 20 + 15 + cur * 30 - r, 20 + r, 20 + 15 + cur * 30 + r
+                             , fill="white", width=1, outline="black")# 绘制标记框
+            if f[0] == gl_data.Xian_index:# 若选择为当前函数则标记
+                f_cv.create_oval(20 - rr, 20 + 15 + cur * 30 - rr, 20 + rr, 20 + 15 + cur * 30 + rr
+                                 , fill="black", width=1, outline="black")
+            # 绘制切换按钮,单击则将当前使用函数切换为该函数
+            button = tk.Button(F_root, text=f[2] + ' ' + f[1], bd=0, bg="white", font=("微软雅黑", 12)
+                               , command=lambda x=f[0]: change_f(x), anchor=W)
+            button.place(x=40, y=20 + cur * 30, width=300, height=30)
+            cur += 1#计数加一
+
+def close_window():
+    sys.exit()
+def main():
+    global Q_root, F_root,root_window
+    gl_data.X = []
+    gl_data.X = []
+    window()
+    # 函数选择相关界面
+    F_root = tk.Frame(root_window, width=400, height=330, bg='white', )
+    F_root.place(x=490, y=60)
+    # 象限选择相关界面
+    Q_root = tk.Frame(root_window, width=400, height=50, bg='white', )
+    Q_root.place(x=20, y=410)
+    function.f_read()
+    buttons()
+    f_button()
+    q_button()
+    show_fit()
+    tk.Button(root_window, text="新增拟合曲线类型", bd=4, command=addfunc).place(x=740, y=12)
+    root_window.protocol("WM_DELETE_WINDOW", close_window)
+    root_window.mainloop()
+if __name__ == '__main__':
+    main()
+    pass

data.py

@@ -0,0 +1,129 @@
+# -*- encoding: utf-8 -*-
+"""
+ @Author: packy945
+ @FileName: data.py
+ @DateTime: 2023/5/31 11:42
+ @SoftWare: PyCharm
+"""
+import tkinter as tk
+from tkinter import *
+import random
+import numpy as np
+
+X = []                  # 等待拟合的x值
+Y = []                  # 等待拟合的y值
+global Canvas2          # 用于显示函数的画布
+Img1 = None             # 绘制的dot.png图像
+Img2 = None             # 绘制的line.png图像
+Xian_index = 0          # 当前选择的函数编号
+Quadrant = 0            # 当前选择的象限信息0为四象限，1为一象限
+MAXV = 1000             # 最大值
+Out = ''                # 拟合输出信息
+LOW = -MAXV             # 坐标轴显示上界
+HIGH = MAXV             # 坐标轴显示下界
+
+
+def random_points():
+    x=[]
+    y=[]
+    for i in range(20):
+        x_= random.uniform(0, 1000)#生成随机浮点数
+        y_= random.uniform(0, 1000)#生成随机浮点数
+        x.append(x_) #加入列表
+        y.append(y_)
+    x=np.array(x) #列表转数组
+    y=np.array(y)
+    arr = np.array(list(zip(x, y)))# 将两个一维数组拼接成二维数组
+    return arr
+
+def compute_curveData(num, step, coefficient):#coefficient代表二次函数系数，数组形式
+    def quadratic_function(x):#构造二次函数y = a * X^2 + b * X + C
+        return coefficient[0] * x ** 2 + coefficient[1] * x + coefficient[2]
+    x_values = np.arange(-num, num, step)
+    y_values = quadratic_function(x_values)#调用quadratic_function(x)函数得到y值
+    curve_data = np.column_stack((x_values, y_values))#将两个一维数组堆叠成二维数组，形成(x,y)的形式
+    return curve_data
+
+
+# #################################拟合优度R^2的计算######################################
+def __sst(y_no_fitting):
+    """
+    计算SST(total sum of squares) 总平方和
+    :param y_no_predicted: List[int] or array[int] 待拟合的y
+    :return: 总平方和SST
+    """
+    y_mean = sum(y_no_fitting) / len(y_no_fitting)
+    s_list =[(y - y_mean)**2 for y in y_no_fitting]
+    sst = sum(s_list)
+    return sst
+
+
+def __ssr(y_fitting, y_no_fitting):
+    """
+    计算SSR(regression sum of squares) 回归平方和
+    :param y_fitting: List[int] or array[int]  拟合好的y值
+    :param y_no_fitting: List[int] or array[int] 待拟合y值
+    :return: 回归平方和SSR
+    """
+    y_mean = sum(y_no_fitting) / len(y_no_fitting)
+    s_list =[(y - y_mean)**2 for y in y_fitting]
+    ssr = sum(s_list)
+    return ssr
+
+
+def __sse(y_fitting, y_no_fitting):
+    """
+    计算SSE(error sum of squares) 残差平方和
+    :param y_fitting: List[int] or array[int] 拟合好的y值
+    :param y_no_fitting: List[int] or array[int] 待拟合y值
+    :return: 残差平方和SSE
+    """
+    s_list = [(y_fitting[i] - y_no_fitting[i])**2 for i in range(len(y_fitting))]
+    sse = sum(s_list)
+    return sse
+
+
+def goodness_of_fit(y_fitting, y_no_fitting):
+    """
+    计算拟合优度R^2
+    :param y_fitting: List[int] or array[int] 拟合好的y值
+    :param y_no_fitting: List[int] or array[int] 待拟合y值
+    :return: 拟合优度R^2
+    """
+    ssr = __ssr(y_fitting, y_no_fitting)
+    sst = __sst(y_no_fitting)
+    rr = ssr /sst
+    return rr
+
+def least_sqaure(x,y):
+    n = len(x)
+    sumx, sumy, sumxy, sumxx = 0, 0, 0, 0
+    for i in range(0, n):
+        sumx += x[i]
+        sumy += y[i]
+        sumxx += x[i] * x[i]
+        sumxy += x[i] * y[i]
+    a = (n * sumxy - sumx * sumy) / (n * sumxx - sumx * sumx)
+    b = (sumxx * sumy - sumx * sumxy) / (n * sumxx - sumx * sumx)
+    return a, b
+import  time
+
+def gradient_descent(x, y):
+    s = time.time()
+    x = 10000 * np.random.randn(1)  # 产生服从正太分布的一个数(均值=0，方差=1)，扩大10000倍
+    eta = 0.09
+    i = 1
+    while True:
+        y = x ^ 2 / 2 - 2 * x
+        x -= eta * 2 * x
+        if y <= 0.0001:
+            print('x is %.6f\ny is %.6f\nand steps are %d' % (x, y, i))
+            break
+        i += 1
+    e = time.time()
+    print('time is %.4f second' % (e - s))
+
+
+if __name__ == '__main__':
+    random_points()
+    pass

fitting.py

@@ -0,0 +1,117 @@
+# -*- encoding: utf-8 -*-
+"""
+ @Author: packy945
+ @FileName: fitting.py
+ @DateTime: 2023/5/31 14:16
+ @SoftWare: PyCharm
+"""
+
+import numpy as np
+import matplotlib.pyplot as plt
+from scipy.optimize import curve_fit
+import pylab as mpl
+from tkinter import *
+import mpl_toolkits.axisartist as axisartist
+import data as gl_data
+import function
+
+mpl.rcParams['font.sans-serif'] = ['SimHei']  # 解决中文不显示问题
+plt.rcParams['axes.unicode_minus'] = False       #解决负数坐标显示问题
+
+def draw_axis(low, high, step=250):
+    fig = plt.figure(figsize=(4.4, 3.2))
+    ax = axisartist.Subplot(fig, 111)# 使用axisartist.Subplot方法创建一个绘图区对象ax
+    fig.add_axes(ax)# 将绘图区对象添加到画布中
+    ax.axis[:].set_visible(False)# 通过set_visible方法设置绘图区所有坐标轴隐藏
+    ax.axis["x"] = ax.new_floating_axis(0, 0)# 添加新的x坐标轴
+    ax.axis["x"].set_axisline_style("-|>", size=1.0)# 给x坐标轴加上箭头
+    ax.axis["y"] = ax.new_floating_axis(1, 0)# 添加新的y坐标轴
+    ax.axis["y"].set_axisline_style("-|>", size=1.0)# y坐标轴加上箭头
+    ax.axis["x"].set_axis_direction("bottom")# 设置x、y轴上刻度显示方向
+    ax.axis["y"].set_axis_direction("left")# 设置x、y轴上刻度显示方向
+    plt.xlim(low, high)  # 把x轴的刻度范围设置
+    plt.ylim(low, high) # 把y轴的刻度范围设置
+    ax.set_xticks(np.arange(low, high + 5, step))# 把x轴的刻度间隔设置
+    ax.set_yticks(np.arange(low, high + 5, step))# 把y轴的刻度间隔设置
+
+def generate_and_plot_sample_data(low, high):
+    num_samples = 25#设置样本点数量
+    gl_data.X = np.random.randint(low=low, high=high, size=num_samples)#随机生成x值
+    gl_data.Y = np.random.randint(low=low, high=high, size=num_samples)#随机生成y值
+    draw_axis(low, high)#绘制坐标轴
+    plt.scatter(gl_data.X, gl_data.Y, color='red')  # 绘制样本数据点
+    plt.savefig(r"dot.png", facecolor='w')#保存到本地
+    plt.close()#清除内存
+    set_phtot(1)#显示到主界面
+
+# 显示数据集
+def selfdata_show(x, y, low, high):# 显示数据集
+    num_points = len(x)  # 样本数据点的数量
+    colors = np.random.rand(num_points, 3)# 生成随机颜色
+    draw_axis(low, high)
+    plt.scatter(x, y, c=colors)# 绘制样本数据点
+    plt.savefig(r"dot.png", facecolor='w')  # 保存为png文件
+    plt.clf()
+    set_phtot(1)
+
+def draw_line(xian_index, low, high, sx, sy):
+    draw_axis(low, high)#绘制坐标轴
+    popt = []#初始化curve_fit
+    pcov = []#初始化curve_fit
+    cur = function.Fun[xian_index]  # 装载正在选择的函数
+    func = cur.get_fun()#获取当前函数func
+    popt, pcov = curve_fit(func, sx, sy)# 用curve_fit来对点进行拟合
+    curve_x = np.arange(low, high)#按照步长生成的一串数字
+    curve_y = [func(i, *popt) for i in curve_x]# 根据x0(按照步长生成的一串数字)来计算y1值
+    plt.plot(curve_x, curve_y, color='blue', label='Fitted Curve')#绘制拟合曲线
+    plt.legend()
+    # plt.show()#显示函数图像
+    plt.savefig(r"line.png", facecolor='w')#将图片保存到本地
+    plt.close()#清除内存
+    set_phtot(2)#将图片显示到程序中
+
+def draw_dots_and_line(xian_index, low, high, sx, sy):
+    ############## begin #####################
+    draw_axis(low, high)
+    popt = []
+    pcov = []
+    cur = function.Fun[xian_index]  # 装载正在选择的函数
+    func = cur.get_fun()#获取当前函数func
+    popt, pcov = curve_fit(func, sx, sy)# 用curve_fit来对点进行拟合
+    positive_mask = sy >= 0.0#给样本点分类
+    negative_mask = sy < 0.0#给样本点分类
+    positive_colors = ['red' if x >= 0.0 else 'blue' for x in sx]#给样本点分类
+    negative_colors = ['green' if x >= 0.0 else 'purple' for x in sx]#给样本点分类
+    #根据样本点类型决定样本点颜色
+    plt.scatter(gl_data.X[positive_mask], gl_data.Y[positive_mask], color=np.array(positive_colors)[positive_mask], lw=1)
+    plt.scatter(gl_data.X[negative_mask], gl_data.Y[negative_mask], color=np.array(negative_colors)[negative_mask], lw=1)
+    curve_x = np.arange(low, high)#按照步长生成的一串数字
+    curve_y = [func(i, *popt) for i in curve_x]# 根据x0(按照步长生成的一串数字)来计算y1值
+    ############## end #######################
+    plt.plot(curve_x, curve_y, color='blue', label='Fitted Curve')#绘制拟合曲线
+    plt.legend()
+    plt.savefig(r"line.png", facecolor='w')#将图片保存到本地
+    plt.close()#清除内存
+    set_phtot(2)#将图片显示到程序中
+
+
+
+def set_phtot(index1):
+    # 显示图像
+    Canvas2 = gl_data.Canvas2
+    if index1 == 1:
+        gl_data.Img1=PhotoImage(file=r"dot.png")
+        # print(gl_data.Img1)
+        set_img1=Canvas2.create_image(2, 10, image=gl_data.Img1, anchor=NW)
+        Canvas2.update()
+        print("已输出数据点")
+    elif index1 == 2:
+        gl_data.Img2=PhotoImage(file=r"line.png")
+        # print(gl_data.Img2)
+        set_img2=Canvas2.create_image(2, 10, image=gl_data.Img2, anchor=NW)
+        Canvas2.update()
+        print("已输出数据点和曲线")
+if __name__ == '__main__':
+    # random_points()
+
+    pass

function.py

@@ -0,0 +1,137 @@
+# -*- encoding: utf-8 -*-
+"""
+ @Author: packy945
+ @FileName: function.py
+ @DateTime: 2023/6/6 14:45
+ @SoftWare: PyCharm
+"""
+import numpy as np
+import math
+import data
+import pandas as pd
+from pandas import DataFrame
+# 函数库
+Show = []
+Fun = []
+Fit_type_library = {}
+class Function:
+    def __init__(self, no, name, v, fun, complete='', demo=''):
+        # 函数名称
+        self.name = name
+        # 变量个数
+        self.variable = v
+        self.function = fun
+        # 函数编号
+        self.no = no
+        # 是否显示
+        self.show = 0
+        # 完整函数
+        self.complete = complete
+        # self.print = ''
+        self.demo = demo
+    def get_fun(self):
+        if self.variable == 2:
+            return self.fun2
+        elif self.variable == 3:
+            return self.fun3
+        elif self.variable == 4:
+            return self.fun4
+        elif self.variable == 5:
+            return self.fun5
+        elif self.variable == 6:
+            return self.fun6
+
+    def fun2(self, x, a0, a1):
+        return eval(self.function)
+
+    def fun3(self, x, a0, a1, a2):
+        return eval(self.function)
+
+    def fun4(self, x, a0, a1, a2, a3):
+        return eval(self.function)
+
+    def fun5(self, x, a0, a1, a2, a3, a4):
+        return eval(self.function)
+
+    def fun6(self, x, a0, a1, a2, a3, a4, a5):
+        return eval(self.function)
+
+    def print_f(self, a):
+        # print('self.show='+self.complete)
+        exec('self.show='+self.complete)
+        # print(self.show)
+        return self.show
+def f_init():
+    cur = 0 # 函数编号
+    # 一次函数
+    newfun = Function(cur, '一次函数', 2, 'a0*x+a1', "f'{a[0]}x+{a[1]}'", 'ax+b')
+    newfun.show = 1
+    Fun.append(newfun)
+    cur += 1
+    # 二次函数
+    newfun = Function(cur, '二次函数', 3, 'a0*x*x+a1*x+a2', "f'{a[0]}x^2+{a[1]}x+{a[2]}'", 'ax^2+bx+c')
+    newfun.show = 1
+    Fun.append(newfun)
+    cur += 1
+    # 三次函数
+    newfun = Function(cur, '三次函数', 4, 'a0*x*x*x+a1*x*x+a2*x+a3', "f'{a[0]}x^3+{a[1]}x^2+{a[2]}x+{a[3]}'", 'ax^3+bx^2+cx+d')
+    newfun.show = 0
+    Fun.append(newfun)
+    cur += 1
+    # 四次函数
+    newfun = Function(cur, '四次函数', 5, 'a0*x*x*x*x+a1*x*x*x+a2*x*x+a3*x+a4'
+                      , "f'{a[0]}x^4+{a[1]}x^3+{a[2]}x^2+{a[3]}x+{a[4]}'", 'ax^4+bx^3+cx^2+dx+e')
+    newfun.show = 0
+    Fun.append(newfun)
+    cur += 1
+    # 指数函数
+    newfun = Function(cur, '指数函数', 2, 'a0*np.exp(0.01*x)+a1', "f'{a[0]}e^(0.01x)+{a[1]}'", 'a*e^(0.01x)+b')
+    newfun.show = 0
+    Fun.append(newfun)
+    cur += 1
+    # 对数函数
+    newfun = Function(cur, '对数函数', 3, 'a0*(np.log(x) + 1e-5) / (np.log(a1) + 1e-5) + a2',
+                      "f'{a[0]}log(x,{a[1]})+{a[2]}'", 'alog(x,b)+c')
+    newfun.show = 0
+    Fun.append(newfun)
+    cur += 1
+    # 高斯函数
+
+# F_init()
+def write():
+    file_path = 'functions.xlsx'#设置路径
+    df = pd.read_excel(io=file_path, header=1)#设置表格
+    print(df)
+    df.columns = ['no', 'name', 'variable', 'function', 'complete', 'demo', 'show']#设置表格标题
+    cur = 0#重置计数
+    for f in Fun:#遍历函数类型
+        df.loc[cur] = [cur, f.name, f.variable, f.function, f.complete, f.demo, f.show]#写进表格
+        cur += 1#计数加一
+    DataFrame(df).to_excel(file_path, sheet_name='Sheet1', index=False, header=True)#保存xlsx
+
+
+def f_read():
+    file_path = 'functions.xlsx'#设置路径
+    df = pd.read_excel(io=file_path, header=0)#设置表格
+    cur = 0
+    for i in range(len(df)):#逐行读取excel
+        newfun = Function(df.loc[i][0], df.loc[i][1], df.loc[i][2], df.loc[i][3], df.loc[i][4], df.loc[i][5])
+        newfun.show = df.loc[i][6]
+        Show.append(df.loc[i][6])#读取函数显示信息
+        Fun.append(newfun)#读取函数信息并添加
+        cur += 1
+    for f in Fun:#建立简表fit_type_library
+        Fit_type_library[f.name] = [f.no, f.demo, f.name]
+if __name__ == '__main__':
+    f_read()
+    # for f in fun:
+    #     print([f.no, f.demo, f.name])
+    for f in Fun:
+        Fit_type_library[f.name] = [f.no, f.demo, f.name]
+
+    print(Fit_type_library)
+    a = [1,2,3,4,5]
+    x = 2
+
+
+    pass

input.py

@@ -0,0 +1,83 @@
+# -*- encoding: utf-8 -*-
+"""
+ @Author: packy945
+ @FileName: input.py
+ @DateTime: 2023/7/19 16:59
+ @SoftWare: PyCharm
+"""
+import tkinter as tk
+
+import numpy as np
+
+import data as gl_data
+from tkinter import *
+global top
+def input_num(root_tk):
+    global top
+    top = tk.Toplevel(root_tk)
+    label1 = Label(top, text="坐标点个数")
+    label1.grid(row=0)  # 这里的side可以赋值为LEFT  RTGHT TOP  BOTTOM
+    num1 = IntVar()
+    entry1 = Entry(top, textvariable=num1)
+    num1.set(0)
+    entry1.grid(row=0, column=1)
+    Label(top, text=" ").grid(row=0, column=3)
+    Button(top, text="确定", command=lambda: input_data(root_tk, int(entry1.get()))).grid(row=0, column=3)
+    top.mainloop()
+def input_data(root_tk, num):
+    global top
+    sample_x = []
+    sample_y = []
+    sample_data = []
+    top.destroy()
+    top = tk.Toplevel(root_tk)
+    def add_sample_data():
+        try:
+            x = float(entry_x.get())
+            y = float(entry_y.get())
+        except:
+            label_status.config(text="输入不合法")
+            return
+        entry_x.delete(0, tk.END)
+        entry_y.delete(0, tk.END)
+        if min(x, y) < gl_data.low or max(x, y) > gl_data.high:
+            label_status.config(text="输入超过范围")
+            return
+        elif len(sample_data) < num:
+            label_status.config(text="点对已添加")
+            sample_data.append((x, y))
+            sample_x.append(x)
+            sample_y.append(y)
+        else:
+            label_status.config(text="已达到最大数量")
+    def check_sample_data():
+        if len(sample_data) == num:
+            label_status.config(text="已达到最大数量")
+            gl_data.x = np.array(sample_x)
+            gl_data.y = np.array(sample_y)
+            print('已添加', sample_data)
+            top.destroy()
+        else:
+            label_status.config(text="还需输入{}个点对".format(num - len(sample_data)))
+            print(sample_data)
+
+    label_x = tk.Label(top, text="X 值：")
+    label_x.pack()
+    entry_x = tk.Entry(top)
+    entry_x.pack()
+    label_y = tk.Label(top, text="Y 值：")
+    label_y.pack()
+    entry_y = tk.Entry(top)
+    entry_y.pack()
+    button_add = tk.Button(top, text="添加", command=add_sample_data)
+    button_add.pack()
+    button_check = tk.Button(top, text="检查", command=check_sample_data)
+    button_check.pack()
+    label_status = tk.Label(top, text="")
+    label_status.pack()
+    top.mainloop()
+
+
+if __name__ == '__main__':
+    root = tk.Tk()
+    input_num(root)

test/一次函数.txt

@@ -0,0 +1,30 @@
+-1000.000000 -303.919733
+-934.000000 -350.424580
+-868.000000 -193.369993
+-802.000000 -474.832293
+-736.000000 -101.068322
+-670.000000 -33.916365
+-604.000000 -164.504704
+-538.000000 -147.298119
+-472.000000 -124.814141
+-406.000000 -139.033018
+-340.000000 -69.265051
+-274.000000 -90.553084
+-208.000000 -114.709905
+-142.000000 -103.201058
+-76.000000 -108.245882
+-10.000000 56.710600
+56.000000 18.503031
+122.000000 185.633626
+188.000000 152.615324
+254.000000 47.216669
+320.000000 256.009421
+386.000000 270.790257
+452.000000 61.971014
+518.000000 121.635726
+584.000000 163.906089
+650.000000 166.204626
+716.000000 315.640621
+782.000000 425.649206
+848.000000 454.347899
+914.000000 289.943295

test/三次函数.txt

@@ -0,0 +1,30 @@
+-1000.000000 -2412.037897
+-934.000000 -1906.704565
+-868.000000 -1515.407287
+-802.000000 -1286.984468
+-736.000000 -991.348043
+-670.000000 -699.579002
+-604.000000 -834.074507
+-538.000000 -694.557977
+-472.000000 -503.237387
+-406.000000 -288.033015
+-340.000000 -248.449961
+-274.000000 -317.763223
+-208.000000 -254.540871
+-142.000000 -269.952677
+-76.000000 -252.274149
+-10.000000 -373.987676
+56.000000 -129.655207
+122.000000 -325.928443
+188.000000 -98.240616
+254.000000 -325.921235
+320.000000 -161.796895
+386.000000 96.648543
+452.000000 -245.636986
+518.000000 190.848311
+584.000000 225.026237
+650.000000 317.523583
+716.000000 772.606080
+782.000000 645.906241
+848.000000 1091.495759
+914.000000 1225.588183

test/二次函数.txt

@@ -0,0 +1,30 @@
+-1000.000000 1318.415137
+-934.000000 971.366429
+-868.000000 950.320306
+-802.000000 635.325663
+-736.000000 774.823634
+-670.000000 659.035975
+-604.000000 449.284057
+-538.000000 262.096521
+-472.000000 141.521962
+-406.000000 65.441983
+-340.000000 162.273141
+-274.000000 209.914028
+-208.000000 62.504373
+-142.000000 -160.439640
+-76.000000 -201.140961
+-10.000000 -178.764894
+56.000000 -194.056288
+122.000000 -221.386689
+188.000000 -236.245098
+254.000000 -317.086262
+320.000000 -385.718988
+386.000000 -198.736083
+452.000000 -256.246461
+518.000000 -226.361577
+584.000000 -329.214396
+650.000000 98.251218
+716.000000 -132.314476
+782.000000 62.741428
+848.000000 120.654860
+914.000000 356.397702

test/四次函数.txt

@@ -0,0 +1,30 @@
+-1000.000000 6580.374854
+-934.000000 5230.299130
+-868.000000 4064.603309
+-802.000000 2824.002023
+-736.000000 2151.187862
+-670.000000 1341.067791
+-604.000000 997.401541
+-538.000000 512.994167
+-472.000000 103.881466
+-406.000000 85.927912
+-340.000000 -256.482213
+-274.000000 -97.197686
+-208.000000 -264.665117
+-142.000000 -237.702195
+-76.000000 -151.105677
+-10.000000 -130.269796
+56.000000 -102.814456
+122.000000 -62.662181
+188.000000 -357.518806
+254.000000 -149.197016
+320.000000 -350.461131
+386.000000 -264.914106
+452.000000 -94.032078
+518.000000 -188.344844
+584.000000 -60.854287
+650.000000 85.277762
+716.000000 413.822510
+782.000000 695.033449
+848.000000 1169.069640
+914.000000 1762.153163

test/对数.txt

@@ -0,0 +1,16 @@
+1.000000 -14.349565
+67.000000 321.611473
+133.000000 375.298867
+199.000000 386.511032
+265.000000 408.069269
+331.000000 423.359694
+397.000000 435.982565
+463.000000 458.199244
+529.000000 451.417416
+595.000000 471.376855
+661.000000 484.015127
+727.000000 489.640132
+793.000000 500.047206
+859.000000 499.698564
+925.000000 492.870266
+991.000000 509.779156

test/指数函数.txt

@@ -0,0 +1,30 @@
+-1000.000000 282.188733
+-934.000000 -121.080276
+-868.000000 89.565718
+-802.000000 -36.875112
+-736.000000 -2.179209
+-670.000000 -33.756961
+-604.000000 -199.536348
+-538.000000 -50.378169
+-472.000000 7.288867
+-406.000000 197.918480
+-340.000000 18.543165
+-274.000000 -80.038062
+-208.000000 -0.092604
+-142.000000 24.234519
+-76.000000 112.628196
+-10.000000 57.868872
+56.000000 -75.900181
+122.000000 53.411782
+188.000000 14.463053
+254.000000 -157.854773
+320.000000 3.419914
+386.000000 -95.442953
+452.000000 -511.818439
+518.000000 -785.633833
+584.000000 -1377.367723
+650.000000 -2606.119973
+716.000000 -5115.078474
+782.000000 -9770.399635
+848.000000 -19298.079697
+914.000000 -37316.681269