如何从 2 个或更多矩阵的所有可能组合创建矩阵？

Question

假设有两个矩阵：

A <- B <- diag(3)  
> A
     [,1] [,2] [,3]
[1,]    1    0    0
[2,]    0    1    0
[3,]    0    0    1

我想创建一个新矩阵 AB，它由 A 和 B 行的所有可能组合组成。预期结果：

> AB
      [,1] [,2] [,3] [,4] [,5] [,6]
 [1,]    1    0    0    1    0    0
 [2,]    1    0    0    0    1    0
 [3,]    1    0    0    0    0    1
 [4,]    0    1    0    1    0    0
 [5,]    0    1    0    0    1    0
 [6,]    0    1    0    0    0    1
 [7,]    0    0    1    1    0    0
 [8,]    0    0    1    0    1    0
 [9,]    0    0    1    0    0    1

如何有效地做到这一点？它可以扩展到两个以上的矩阵吗？

Answer 1

您可以使用expand.grid()并获取其输出来索引矩阵 A 和 B，

x <- expand.grid(1:3,1:3)

cbind(A[x[,1],], B[x[,2],])

给，

     [,1] [,2] [,3] [,4] [,5] [,6]
 [1,]    1    0    0    1    0    0
 [2,]    0    1    0    0    1    0
 [3,]    0    0    1    0    0    1
 [4,]    1    0    0    1    0    0
 [5,]    0    1    0    0    1    0
 [6,]    0    0    1    0    0    1
 [7,]    1    0    0    1    0    0
 [8,]    0    1    0    0    1    0
 [9,]    0    0    1    0    0    1

编辑：

对于两个以上的矩阵，您可以使用如下函数，

myfun <- function(...) {

     arguments <- list(...)

     a <- expand.grid(lapply(arguments, function(x) 1:nrow(x)))
    
    
     do.call(cbind,lapply(seq(a),function(x) { arguments[[x]][a[,x],] }))

 
}

out <- myfun(A,B,C)

head(out)

给，

     [,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8] [,9] [,10]
[1,]    1    0    0    1    0    0    1    0    0     0
[2,]    0    1    0    1    0    0    1    0    0     0
[3,]    0    0    1    1    0    0    1    0    0     0
[4,]    1    0    0    0    1    0    1    0    0     0
[5,]    0    1    0    0    1    0    1    0    0     0
[6,]    0    0    1    0    1    0    1    0    0     0

数据：

A <- B <- diag(3)
C <- diag(4)