热图与伪彩色

# ===== 示例1：使用seaborn绘制热图 =====
import numpy as np
import pandas as pd
import seaborn as sns
import matplotlib.pyplot as plt
from sklearn.datasets import load_iris

# 加载鸢尾花数据
iris = load_iris()
X = iris.data
feature_names = ['Sepal length, $X_1$', 'Sepal width, $X_2$',
                 'Petal length, $X_3$', 'Petal width, $X_4$']

# 转换为DataFrame
X_df = pd.DataFrame(X, columns=feature_names)

# 绘制热图
fig, ax = plt.subplots(figsize=(3, 4))
sns.heatmap(X_df,
           cmap='RdYlBu_r',           # 色谱
           xticklabels=list(X_df.columns),
           yticklabels=False,         # 关闭纵轴标签
           cbar_kws={"orientation": "vertical"},
           vmin=0, vmax=8)
plt.title('Iris Dataset')
plt.show()


# ===== 示例2：聚类热图（带树状图） =====
sns.clustermap(X_df,
              cmap='RdYlBu_r',
              xticklabels=list(X_df.columns),
              yticklabels=False,
              figsize=(3, 6),
              vmin=0, vmax=8)
plt.show()


# ===== 示例3：格拉姆矩阵可视化 =====
# 计算格拉姆矩阵 G = X^T @ X
G = X.T @ X

fig, axs = plt.subplots(1, 5, figsize=(8, 3),
                       gridspec_kw={'width_ratios': [3, 0.5, 3, 0.5, 3]})

# G矩阵
plt.sca(axs[0])
sns.heatmap(G, cmap='RdYlBu_r',
           vmax=5000, vmin=0,
           annot=True, fmt=".0f",
           cbar_kws={'orientation': 'horizontal'},
           yticklabels=False,
           square='equal')
plt.title('$G$')

# 等号
plt.sca(axs[1])
plt.title('=')
plt.axis('off')

# X^T
plt.sca(axs[2])
sns.heatmap(X.T, cmap='RdYlBu_r',
           vmax=8, vmin=0,
           cbar_kws={'orientation': 'horizontal'},
           xticklabels=False,
           yticklabels=False)
plt.title('$X^T$')

# @符号
plt.sca(axs[3])
plt.title('@')
plt.axis('off')

# X
plt.sca(axs[4])
sns.heatmap(X, cmap='RdYlBu_r',
           vmax=8, vmin=0,
           cbar_kws={'orientation': 'horizontal'},
           xticklabels=False,
           yticklabels=False)
plt.title('$X$')
plt.show()


# ===== 示例4：Cholesky分解可视化 =====
# G = L @ L^T
L = np.linalg.cholesky(G)

fig, axs = plt.subplots(1, 5, figsize=(8, 3),
                       gridspec_kw={'width_ratios': [3, 0.5, 3, 0.5, 3]})

plt.sca(axs[0])
sns.heatmap(G, cmap='RdYlBu_r',
           vmax=5000, vmin=0,
           annot=True, fmt=".0f",
           square='equal')
plt.title('$G$')

plt.sca(axs[1])
plt.title('=')
plt.axis('off')

plt.sca(axs[2])
sns.heatmap(L, cmap='RdYlBu_r',
           annot=True,
           xticklabels=False,
           yticklabels=False)
plt.title('$L$')

plt.sca(axs[3])
plt.title('@')
plt.axis('off')

plt.sca(axs[4])
sns.heatmap(L.T, cmap='RdYlBu_r',
           annot=True,
           xticklabels=False,
           yticklabels=False)
plt.title('$L^T$')
plt.show()


# 💡 关键学习点：
# 1. seaborn.heatmap()：快速绘制热图，自动配色
# 2. clustermap()：带层次聚类的热图，自动排序
# 3. annot=True：在单元格中显示数值
# 4. cmap参数：选择色谱（RdYlBu_r红黄蓝翻转）
# 5. vmin/vmax：控制色谱范围，保证对比度