在R中,如何将矩阵的不同边缘上的累积和的计算推广到多维数组?
例如,给定矩阵
a2 <- array(1:6, dim = c(2,3))
[,1] [,2] [,3] [1,] 1 3 5 [2,] 2 4 6
可以使用apply
计算不同边距的累积总和:
apply(a2, 2, cumsum)
[,1] [,2] [,3] [1,] 1 3 5 [2,] 3 7 11
t(apply(a2, 1, cumsum))
[,1] [,2] [,3] [1,] 1 4 9 [2,] 2 6 12
请注意,在后一种情况下需要进行一些整形。现在的问题是:
您如何计算多维数组的累积和?
例如,对于三维数组,如:
a3 <- array(1:24, dim = c(2,3,4))
我对行,列和第三维的累积和感兴趣,保留了原始数组的结构。具体来说,行累积总和应为:
, , 1 [,1] [,2] [,3] [1,] 1 4 9 [2,] 2 6 12 , , 2 [,1] [,2] [,3] [1,] 7 16 27 [2,] 8 18 30 , , 3 [,1] [,2] [,3] [1,] 13 28 45 [2,] 14 30 48 , , 4 [,1] [,2] [,3] [1,] 19 40 63 [2,] 20 42 66
n维数组的答案是什么?
一种方法是使用一个很好的旧for
循环
res <- a3
for (k in 1:dim(a3)[3]) res[, , k] <- t(apply(a3[, , k], 1, cumsum))
res
#, , 1
#
# [,1] [,2] [,3]
#[1,] 1 4 9
#[2,] 2 6 12
#
#, , 2
#
# [,1] [,2] [,3]
#[1,] 7 16 27
#[2,] 8 18 30
#
#, , 3
#
# [,1] [,2] [,3]
#[1,] 13 28 45
#[2,] 14 30 48
#
#, , 4
#
# [,1] [,2] [,3]
#[1,] 19 40 63
#[2,] 20 42 66
这几乎给出了你想要的但结果是转置的
apply(a3, c(1, 3), cumsum)
#, , 1
# [,1] [,2]
#[1,] 1 2
#[2,] 4 6
#[3,] 9 12
#, , 2
# [,1] [,2]
#[1,] 7 8
#[2,] 16 18
#[3,] 27 30
#, , 3
# [,1] [,2]
#[1,] 13 14
#[2,] 28 30
#[3,] 45 48
#, , 4
# [,1] [,2]
#[1,] 19 20
#[2,] 40 42
#[3,] 63 66
我不知道如何在同一个apply
调用中转换结果(应该有一种方法)。我试过了
t(apply(a3, c(1, 3), cumsum))
apply(a3, c(1, 3), function(x) t(cumsum(x)))
但这不起作用。但是,现在如果我们再次使用apply
并进行转置,我们可以恢复原始结构。
apply(apply(a3, c(1, 3), cumsum), c(1, 3), t)
使用apply
,然后使用aperm
。唯一棘手的部分是获得正确的利润:
aperm(apply(a3, -2, cumsum), c(2, 1, 3))
其中每一项都有效:
aperm(apply(a3, c(1, 3), cumsum), c(2, 1, 3))
aperm(apply(a3, c(3, 1), cumsum), c(3, 1, 2))
apply(apply(a3, -2, cumsum), -2, c)
apply(apply(a3, c(1, 3), cumsum), c(1, 3), c)
library(plyr)
aa <- aperm(aaply(a3, c(1, 3), cumsum), c(1, 3, 2))
dimnames(aa) <- NULL
从@G推断。格洛腾迪克的答案,这个函数使用aperm
来计算n维数组的任何边界上的累积和:
array_cumsum <- function(a, margin) {
n <- length(dim(a))
permorder <- append(x = 2:n, 1, margin - 1)
aperm(apply(a, -margin, cumsum), permorder)
}
例如,使用一个简单的数组来轻松地计算累积和,该函数可用于计算第二维上的余量:
a <- array(1, dim = c(2,3,4))
array_cumsum(a3, 2)
# , , 1
#
# [,1] [,2] [,3]
# [1,] 1 2 3
# [2,] 1 2 3
#
# , , 2
#
# [,1] [,2] [,3]
# [1,] 1 2 3
# [2,] 1 2 3
#
# , , 3
#
# [,1] [,2] [,3]
# [1,] 1 2 3
# [2,] 1 2 3
#
# , , 4
#
# [,1] [,2] [,3]
# [1,] 1 2 3
# [2,] 1 2 3
以及第三维度:
array_cumsum(a3, 3)
# , , 1
#
# [,1] [,2] [,3]
# [1,] 1 1 1
# [2,] 1 1 1
#
# , , 2
#
# [,1] [,2] [,3]
# [1,] 2 2 2
# [2,] 2 2 2
#
# , , 3
#
# [,1] [,2] [,3]
# [1,] 3 3 3
# [2,] 3 3 3
#
# , , 4
#
# [,1] [,2] [,3]
# [1,] 4 4 4
# [2,] 4 4 4