等高线、网格、三角剖分

# ===== 示例1：等高线原理 =====
import numpy as np
import matplotlib.pyplot as plt
from sympy import lambdify, exp
from sympy.abc import x, y

# 定义peaks函数（MATLAB经典函数）
f_xy = 3*(1-x)**2*exp(-(x**2) - (y+1)**2) \
     - 10*(x/5 - x**3 - y**5)*exp(-x**2-y**2) \
     - 1/3*exp(-(x+1)**2 - y**2)

f_xy_fcn = lambdify([x, y], f_xy)

# 生成网格
xx, yy = np.meshgrid(
    np.linspace(-3, 3, 121),
    np.linspace(-3, 3, 121)
)
ff = f_xy_fcn(xx, yy)

# 三维等高线
fig = plt.figure()
ax = fig.add_subplot(111, projection='3d')

# 绘制曲面网格
ax.plot_wireframe(xx, yy, ff,
                  color=[0.6, 0.6, 0.6],
                  rstride=5, cstride=5,
                  linewidth=0.25)

# 绘制等高线（在z=2的平面）
ax.contour(xx, yy, ff,
          levels=[2],
          colors='b',
          linewidths=1)

ax.set_xlabel('$x_1$')
ax.set_ylabel('$x_2$')
ax.set_zlabel('$f(x_1, x_2)$')
ax.view_init(azim=-120, elev=30)
plt.show()


# ===== 示例2：平面等高线（不同颗粒度） =====
# 低颗粒度（粗糙）
xx_coarse, yy_coarse = np.meshgrid(
    np.linspace(-3, 3, 7),
    np.linspace(-3, 3, 7)
)
ff_coarse = f_xy_fcn(xx_coarse, yy_coarse)

fig, ax = plt.subplots()
ax.scatter(xx_coarse, yy_coarse, marker='.', color='k')
CS = ax.contour(xx_coarse, yy_coarse, ff_coarse,
               levels=np.linspace(-8, 9, 18),
               cmap='RdYlBu_r',
               linewidths=1)
ax.set_xlabel('$x_1$')
ax.set_ylabel('$x_2$')
plt.show()

# 高颗粒度（精细）
xx_fine, yy_fine = np.meshgrid(
    np.linspace(-3, 3, 101),
    np.linspace(-3, 3, 101)
)
ff_fine = f_xy_fcn(xx_fine, yy_fine)

fig, ax = plt.subplots()
CS = ax.contour(xx_fine, yy_fine, ff_fine,
               levels=np.linspace(-8, 9, 18),
               cmap='RdYlBu_r',
               linewidths=1)
ax.clabel(CS, inline=True, fontsize=8)
plt.show()


# ===== 示例3：填充等高线（contourf） =====
fig, ax = plt.subplots()
CS = ax.contourf(xx_fine, yy_fine, ff_fine,
                levels=np.linspace(-8, 8, 17),
                cmap='RdYlBu_r')
fig.colorbar(CS)
ax.set_xlabel('$x_1$')
ax.set_ylabel('$x_2$')
plt.show()


# 💡 关键学习点：
# 1. meshgrid()生成二维网格：点数越多，等高线越平滑
# 2. contour()绘制等高线：levels参数控制等高线数量
# 3. contourf()绘制填充等高线：展示数值分布
# 4. clabel()添加等高线标签：显示具体数值
# 5. 颗粒度影响：网格太粗会导致等高线失真

# ===== 决策边界可视化 =====
import numpy as np
from matplotlib import pyplot as plt
from sklearn import neighbors, datasets
from matplotlib.colors import ListedColormap
from sklearn.naive_bayes import GaussianNB
from sklearn.tree import DecisionTreeClassifier

# 创建色谱（3类分类问题）
cmap_light = ListedColormap(['#FFAAAA', '#AAFFAA', '#AAAAFF'])
cmap_bold = ListedColormap(['#FF0000', '#00FF00', '#0000FF'])

# 加载鸢尾花数据
iris = datasets.load_iris()
X = iris.data[:, :2]  # 只取前两个特征（花萼长度、宽度）
y = iris.target

# 定义绘图网格范围
x_min, x_max = 4, 8
y_min, y_max = 2, 5
xx, yy = np.meshgrid(
    np.linspace(x_min, x_max, 1000),
    np.linspace(y_min, y_max, 100)
)


# ===== 示例1：决策树分类器 =====
clf_tree = DecisionTreeClassifier(max_depth=5)
clf_tree.fit(X, y)

# 预测网格点的类别
Z = clf_tree.predict(np.c_[xx.ravel(), yy.ravel()])
Z = Z.reshape(xx.shape)

# 绘制决策边界（填充等高线）
fig, ax = plt.subplots(figsize=(8, 6))
plt.contourf(xx, yy, Z, cmap=cmap_light)

# 绘制训练样本点
plt.scatter(X[:, 0], X[:, 1], c=y, cmap=cmap_bold)
plt.xlabel('Sepal length (cm)')
plt.ylabel('Sepal width (cm)')
plt.title('Decision Tree Classifier')
plt.axis('tight')
plt.show()


# ===== 示例2：朴素贝叶斯分类器 =====
clf_nb = GaussianNB()
clf_nb.fit(X, y)

Z = clf_nb.predict(np.c_[xx.ravel(), yy.ravel()])
Z = Z.reshape(xx.shape)

fig, ax = plt.subplots(figsize=(8, 6))
plt.contourf(xx, yy, Z, cmap=cmap_light)
plt.scatter(X[:, 0], X[:, 1], c=y, cmap=cmap_bold)
plt.xlabel('Sepal length (cm)')
plt.ylabel('Sepal width (cm)')
plt.title('Gaussian Naive Bayes')
plt.axis('tight')
plt.show()


# ===== 示例3：KNN分类器 =====
clf_knn = neighbors.KNeighborsClassifier(n_neighbors=15)
clf_knn.fit(X, y)

Z = clf_knn.predict(np.c_[xx.ravel(), yy.ravel()])
Z = Z.reshape(xx.shape)

fig, ax = plt.subplots(figsize=(8, 6))
plt.contourf(xx, yy, Z, cmap=cmap_light)
plt.scatter(X[:, 0], X[:, 1], c=y, cmap=cmap_bold, edgecolors='k')
plt.xlabel('Sepal length (cm)')
plt.ylabel('Sepal width (cm)')
plt.title('KNN (k=15) Classifier')
plt.axis('tight')
plt.show()


# 💡 关键学习点：
# 1. contourf()绘制决策边界：展示分类器的决策区域
# 2. meshgrid()生成密集网格：覆盖整个特征空间
# 3. predict()预测每个网格点：确定决策边界
# 4. ListedColormap自定义色谱：区分不同类别
# 5. 决策边界形状反映分类器特性：
#    - 决策树：矩形分割
#    - 朴素贝叶斯：平滑曲线
#    - KNN：局部敏感的边界