对称矩阵中每个单元格中值的组合

Question

我有一个权重向量，我想将其插入到对称矩阵中。我想要所有权重组合（所有位置的所有权重但不在对角线上）

我尝试遍历矩阵，但后来我只得到相同的矩阵三次。（我也找不到它的答案或 public 这个问题的解决方案。）

weight <- seq(0.1, 1, by = 0.1)
C <- matrix(0, nrow = 3, ncol = 3)
for (i in seq_len(nrow(C))) {
  C_old <- C
  for (j in seq_len(i)) {
    if (i == j) {
      C[i, i] <- 0
    } else {
      C_old2 <- C_old
      for (w in weight) {
        C[i, j] <- w
        C[j, i] <- C[i, j]
        C_old[i, j] <- w
        C_old[j, i] <- C_old[i, j]
        C_old2[i, j] <- w
        C_old2[j, i] <- C_old2[i, j]
        iter <- iter + 3
        print(C)
        print(C_old)
        print(C_old2)
      }
   }
}

我想要所有矩阵使得

Matrix 0:

0 0 0
0 0 0
0 0 0 


Matrix 1:

0 0 0
0 0 0.1
0 0.1 0 

Matrix 2:

0 0 0.1
0 0 0.1
0.1 0.1 0 


Matrix 3:

0 0.1 0.1
0.1 0 0.1
0.1 0.1 0 

Matrix 4:

0 0.1 0.1
0.1 0 0.2
0.1 0.2 0 


Matrix n:

0 0.9 0.1
0.5 0 0.5
0.1 0.9 0 


Matrix:

0 x y
z 0 z
y x 0

我希望最后一个矩阵的所有组合是 x、y 和 z 可以是权重中的任何值。

第一个矩阵（全为 0）并不是很重要，所以如果解决方案省略了它我真的不在乎

Answer 1

不知道你想要这个干什么，但给你：

weight <- seq(0.1, 1, by = 0.1)
C <- matrix(0, nrow = 3, ncol = 3)
C_list <- vector("list", 10)

for(i in 1:length(weight)){
  for(j in 1:3){
    if(j == 1){
      C[2,3] <- weight[i]
      C[3,2] <- weight[i]
    }
    if(j == 2){
      C[1,3] <- weight[i]
      C[3,1] <- weight[i]
    }
    if(j == 3){
      C[1,2] <- weight[i]
      C[2,1] <- weight[i]
    }
    C_list[[i]][[j]] <- C
  }
}

结果：

> C_list
[[1]]
[[1]][[1]]
     [,1] [,2] [,3]
[1,]    0  0.0  0.0
[2,]    0  0.0  0.1
[3,]    0  0.1  0.0

[[1]][[2]]
     [,1] [,2] [,3]
[1,]  0.0  0.0  0.1
[2,]  0.0  0.0  0.1
[3,]  0.1  0.1  0.0

[[1]][[3]]
     [,1] [,2] [,3]
[1,]  0.0  0.1  0.1
[2,]  0.1  0.0  0.1
[3,]  0.1  0.1  0.0


[[2]]
[[2]][[1]]
     [,1] [,2] [,3]
[1,]  0.0  0.1  0.1
[2,]  0.1  0.0  0.2
[3,]  0.1  0.2  0.0

[[2]][[2]]
     [,1] [,2] [,3]
[1,]  0.0  0.1  0.2
[2,]  0.1  0.0  0.2
[3,]  0.2  0.2  0.0

...

Answer 2

多亏了 LAP，我改变了方法并设法做到了：

weight <- seq(0.1, 1, by = 0.1)
C <- matrix(0, nrow = 3, ncol = 3)
C_list <- vector("list", 10)
names(C_list) <- as.character(weight)

for(i1 in weight){
  C_list[[as.character(i1)]] <- vector("list", 10)
  names(C_list[[as.character(i1)]]) <- as.character(weight)
  for (i2 in weight){
    C_list[[as.character(i1)]][[as.character(i2)]] <- vector("list", 10)
    names(C_list[[as.character(i1)]][[as.character(i2)]]) <- as.character(weight)
    for (i3 in weight) {
      C[2, 3] <- i1
      C[3, 2] <- i1
      C[1, 3] <- i2
      C[3, 1] <- i2
      C[1, 2] <- i3
      C[2, 1] <- i3
      C_list[[as.character(i1)]][[as.character(i2)]][[as.character(i3)]] <- C
    }
  }
}

现在 C_list 是一个列表的列表列表，每个列表都有一个矩阵。 length(unlist(unlist(C_list, recursive = FALSE), recursive = FALSE)) == 1000 即存在的 10^3 种组合。

对称矩阵中每个单元格中值的组合

Combinations of values in each cell in a symmetric matrix

r

symmetric

matrix