Merge pull request #16 from YasmineLiu/main

good try.

1 Scatter Plot/Fitting trends.py

@@ -0,0 +1,62 @@
+import matplotlib.pyplot as plt
+import numpy as np
+from scipy.interpolate import interp1d
+from scipy.interpolate import make_interp_spline, BSpline
+import statsmodels.api as sm
+lowess = sm.nonparametric.lowess
+
+# 生成示例散点数据（使用正态分布和均匀分布）
+np.random.seed(20)
+x1 = np.sort(10 * np.random.randn(100))  # 正态分布
+x2 = np.sort(10 * np.random.rand(40))   # 均匀分布
+x = np.concatenate([x1, x2])
+
+# 添加更多噪声
+y = 2 * x + 1 + np.sin(x) + 5 * np.random.randn(len(x))
+
+# 对 x 进行排序
+sorted_indices = np.argsort(x)
+x_sorted = x[sorted_indices]
+y_sorted = y[sorted_indices]
+
+# 绘制散点图
+plt.scatter(x, y, label='Basic Data')
+
+# 局部加权散点拟合
+# lowess函数会返回两列numpy数据，第一列是原始数据拟合不平滑的结果，第二列是平滑一下后的数据
+# 其中frac越大，加权散点拟合的效果越平滑
+# missing =  (‘none’, ‘drop’, and ‘raise’) 'none'不进行缺失值检查，'drop'丢弃含有缺失值的样本(默认), 'raise'有缺失值会报错
+# yest0 = lowess(y_sorted,x_sorted)
+yest0 = lowess(y_sorted, x_sorted, frac=1./3.)[:,0]
+yest = lowess(y_sorted, x_sorted, frac=1./3.)[:,1]
+# loess_fit = make_interp_spline(x_sorted, y_sorted, k=3)
+# loess_curve = loess_fit(x_sorted)
+plt.plot(x_sorted, yest0, label='Locally weighted scatter fitting(no smoothy)', color='yellow')
+plt.plot(x_sorted, yest, label='Locally weighted scatter fitting(smoothy)', color='green')
+
+# 线性拟合
+# 1表示这是一条拟合的线性直线
+linear_fit = np.polyfit(x_sorted, y_sorted, 1)
+linear_curve = np.poly1d(linear_fit)
+plt.plot(x_sorted, linear_curve(x_sorted), label='Linear Fitting', color='orange')
+
+# 多项式拟合曲线
+#其中10表示多项式的次数为10次
+poly_fit = np.polyfit(x_sorted, y_sorted, 10)
+poly_curve = np.poly1d(poly_fit)
+x_poly = np.linspace(min(x_sorted), max(x_sorted), 100)
+plt.plot(x_poly, poly_curve(x_poly), label='polynomial fitting Quadratic', color='purple')
+
+# 计算趋势带（可根据需要调整标准差倍数）
+std_dev = np.std(y_sorted)
+upper_band = yest + 2 * std_dev
+lower_band = yest - 2 * std_dev
+
+# 绘制趋势带
+plt.fill_between(x_sorted, upper_band, lower_band, alpha=0.2, color='green', label='trend band')
+
+plt.legend()
+plt.xlabel('X-axis')
+plt.ylabel('Y-axis')
+plt.title('Fitting curves and locally weighted scatter fitting')
+plt.show()