R-给定一个矩阵和一个幂，产生包含矩阵列所有组合的多个矩阵 [英] R - Given a matrix and a power, produce multiple matrices containing all combinations of matrix columns

问题描述

给出一个矩阵mat(大小为N乘以M)和一个幂p(例如4)，产生p矩阵，其中每个p矩阵包含所有可能的矩阵mat中的列在该程度的组合.

Given a matrix mat (of size N by M) and a power, p (e.g., 4), produce p matrices, where each p-th matrix contains all possible combinations of the columns in mat at that degree.

在我当前的方法中，我生成第p个矩阵，然后在下一次调用中使用它来生成第p+1个矩阵.对于给定的电源p，这可以自动化"吗，而不是手动完成?

In my current approach, I generate the p-th matrix and then use it in the next call to produce the p+1th matrix. Can this be 'automated' for a given power p, rather than done manually?

我是R的新手，并且了解实现此解决方案的方法可能比以下尝试更有效，更优雅...

I am a novice when it comes to R and understand that there is likely a more efficient and elegant way to achieve this solution than the following attempt...

N = 5
M = 3
p = 4
mat = matrix(1:(N*M),N,M)
mat_1 = mat
mat_2 = t(sapply(1:N, function(i) tcrossprod(mat_1[i, ], mat[i, ])))
mat_3 = t(sapply(1:N, function(i) tcrossprod(mat_2[i, ], mat[i, ])))
mat_4 = t(sapply(1:N, function(i) tcrossprod(mat_3[i, ], mat[i, ])))

任何人都可以提供一些建议吗?我的目标是为给定的矩阵mat和功效p创建一个函数，以更自动化"的方式输出p不同的矩阵.

Can anyone provide some suggestions? My goal is to create a function for a given matrix mat and power p that outputs the p different matrices in a more 'automated' fashion.

让我开始学习的相关问题:如何用所有组合将两个矩阵的列相乘

Related question that got me started: How to multiply columns of two matrix with all combinations

推荐答案

您可以执行以下操作

N = 5
M = 3
p = 4
mat = matrix(1:(N*M),N,M)

res_mat <- list()
res_mat[[1]] <- mat
for(i in 2:p) {
     res_mat[[i]] <- t(sapply(1:N, function(j) tcrossprod(res_mat[[i-1]][j, ], res_mat[[1]][j, ])))
}

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