如何用Polars实现两个DataFrame逐列滚动计算？

首先构造示例数据：

import polars as pl
import numpy as np

# 生成与示例结构一致的Polars DataFrame
X = pl.DataFrame({f"id{i}": np.random.randn(200) for i in range(100)})
Y = pl.DataFrame({f"id{i}": np.random.randn(200) for i in range(100)})

核心实现思路 #

Polars没有直接提供类似Pandasrolling().cov(Y)这种跨DataFrame的逐列滚动计算API，需要通过合并DataFrame+自定义窗口表达式来实现，核心是基于统计公式手动推导滚动计算逻辑（匹配Pandas默认的ddof=1无偏估计）：

• 滚动协方差：sum((x - x_mean)(y - y_mean)) / (window_size - 1)
• 滚动方差：sum((x - x_mean)²) / (window_size - 1)
• 滚动相关系数：协方差 / (x_std * y_std)
• 滚动斜率：协方差 / x_var

完整代码实现 #

window_size = 5

# 合并X与Y，给Y的列添加前缀避免命名冲突
merged_df = X.hstack(Y.rename({col: f"y_{col}" for col in Y.columns}))

# 生成所有列的滚动计算表达式
expressions = []
for col in X.columns:
    x_col = col
    y_col = f"y_{col}"
    
    # 计算窗口内的X、Y列均值（min_periods匹配Pandas默认行为，仅当窗口满5行时计算）
    x_win_mean = pl.col(x_col).rolling_mean(window_size=window_size, min_periods=window_size)
    y_win_mean = pl.col(y_col).rolling_mean(window_size=window_size, min_periods=window_size)
    
    # 滚动协方差（ddof=1）
    cov = ((pl.col(x_col) - x_win_mean) * (pl.col(y_col) - y_win_mean)).rolling_sum(
        window_size=window_size, min_periods=window_size
    ) / (window_size - 1)
    expressions.append(cov.alias(f"{col}_cov"))
    
    # 滚动X列方差（ddof=1）
    x_var = ((pl.col(x_col) - x_win_mean)**2).rolling_sum(
        window_size=window_size, min_periods=window_size
    ) / (window_size - 1)
    expressions.append(x_var.alias(f"{col}_var"))
    
    # 滚动相关系数
    y_var = ((pl.col(y_col) - y_win_mean)**2).rolling_sum(
        window_size=window_size, min_periods=window_size
    ) / (window_size - 1)
    corr = cov / (x_var.sqrt() * y_var.sqrt())
    expressions.append(corr.alias(f"{col}_corr"))
    
    # 滚动斜率
    slope = cov / x_var
    expressions.append(slope.alias(f"{col}_slope"))

# 执行计算并得到结果
result = merged_df.select(expressions)

结果说明 #

• 结果DataFrame中，每一列对应原始id{i}列的滚动计算结果：id{i}_cov是滚动协方差，id{i}_var是X列的滚动方差，id{i}_corr是滚动相关系数，id{i}_slope是滚动斜率
• 前4行结果为null，与Pandas默认的min_periods=window_size行为一致，仅当窗口包含完整5行数据时才输出有效计算值

内容的提问来源于stack exchange，提问作者c dai