c(x %*% df %*% y) 

#> [1] 0.5

另一种可能的解决方案基于 outer :

sum(outer(x, y, Vectorize(\(x,y) x*y*df[x+1,y+1])))

#> [1] 0.5

x <- c(0, 1)
y <- c(0, 1, 2)
vals<- c(4/24, 6/24, 3/24, 3/24, 4/24, 4/24)
mat <- matrix(vals, byrow = TRUE, nrow = 2, ncol = 3,
              dimnames = list(x,y))  ## not a data frame; don't call it "df"

还有比 for 回路:

sum(tcrossprod(x, y) * mat)
#[1] 0.5

sum((x %o% y) * df)

说明:

x %o% y 获取向量的外积 x 和 y 即:

#>      [,1] [,2] [,3]
#> [1,]    0    0    0
#> [2,]    0    1    2

因为它的尺寸与 df ,您可以将相应的元素相乘,得到总和: sum((x %o% y) * df)

如果你是R新手(和我一样),这里是循环方法。

result = 0
for (i in 1:length(x)) {
  for (j in 1:length(y)) {
    result = result + x[i] * y[j] * df[i, j]
  }
}
result