Permutation matrix

This function create permutation matrices.

Usage

perm_matrix(n, m = 1, unique = FALSE)

Arguments

n

The size of the square matri

m

Number of permutations

unique

Whether to return unique cases

Value

This function returns a list of permutation matrices

Author

Alejandro Espinosa-Rada

Examples

W <- matrix(c(
  0, 1, 0, 0, 0,
  0, 0, 1, 0, 0,
  1, 0, 0, 0, 0,
  0, 0, 0, 0, 1,
  0, 0, 0, 1, 0
), byrow = TRUE, ncol = 5)
rownames(W) <- c("P", "Q", "R", "S", "T")
colnames(W) <- rownames(W)
perm_matrix(5, m = 1000, unique = TRUE)
#> [[1]]
#>      [,1] [,2] [,3] [,4] [,5]
#> [1,]    0    0    0    0    1
#> [2,]    0    0    1    0    0
#> [3,]    1    0    0    0    0
#> [4,]    0    0    0    1    0
#> [5,]    0    1    0    0    0
#> 
#> [[2]]
#>      [,1] [,2] [,3] [,4] [,5]
#> [1,]    1    0    0    0    0
#> [2,]    0    0    1    0    0
#> [3,]    0    0    0    1    0
#> [4,]    0    0    0    0    1
#> [5,]    0    1    0    0    0
#> 
#> [[3]]
#>      [,1] [,2] [,3] [,4] [,5]
#> [1,]    0    1    0    0    0
#> [2,]    1    0    0    0    0
#> [3,]    0    0    1    0    0
#> [4,]    0    0    0    0    1
#> [5,]    0    0    0    1    0
#> 
#> [[4]]
#>      [,1] [,2] [,3] [,4] [,5]
#> [1,]    0    0    0    1    0
#> [2,]    0    0    0    0    1
#> [3,]    1    0    0    0    0
#> [4,]    0    1    0    0    0
#> [5,]    0    0    1    0    0
#> 
#> [[5]]
#>      [,1] [,2] [,3] [,4] [,5]
#> [1,]    1    0    0    0    0
#> [2,]    0    1    0    0    0
#> [3,]    0    0    1    0    0
#> [4,]    0    0    0    1    0
#> [5,]    0    0    0    0    1
#> 
#> [[6]]
#>      [,1] [,2] [,3] [,4] [,5]
#> [1,]    0    0    0    1    0
#> [2,]    0    1    0    0    0
#> [3,]    0    0    1    0    0
#> [4,]    0    0    0    0    1
#> [5,]    1    0    0    0    0
#> 
#> [[7]]
#>      [,1] [,2] [,3] [,4] [,5]
#> [1,]    0    0    0    1    0
#> [2,]    0    1    0    0    0
#> [3,]    0    0    0    0    1
#> [4,]    0    0    1    0    0
#> [5,]    1    0    0    0    0
#> 
#> [[8]]
#>      [,1] [,2] [,3] [,4] [,5]
#> [1,]    0    0    0    0    1
#> [2,]    0    1    0    0    0
#> [3,]    0    0    0    1    0
#> [4,]    0    0    1    0    0
#> [5,]    1    0    0    0    0
#> 
#> [[9]]
#>      [,1] [,2] [,3] [,4] [,5]
#> [1,]    0    0    0    1    0
#> [2,]    1    0    0    0    0
#> [3,]    0    0    0    0    1
#> [4,]    0    1    0    0    0
#> [5,]    0    0    1    0    0
#> 
#> [[10]]
#>      [,1] [,2] [,3] [,4] [,5]
#> [1,]    0    0    0    1    0
#> [2,]    1    0    0    0    0
#> [3,]    0    0    1    0    0
#> [4,]    0    1    0    0    0
#> [5,]    0    0    0    0    1
#> 
#> [[11]]
#>      [,1] [,2] [,3] [,4] [,5]
#> [1,]    1    0    0    0    0
#> [2,]    0    0    0    0    1
#> [3,]    0    1    0    0    0
#> [4,]    0    0    1    0    0
#> [5,]    0    0    0    1    0
#> 
#> [[12]]
#>      [,1] [,2] [,3] [,4] [,5]
#> [1,]    0    1    0    0    0
#> [2,]    0    0    0    1    0
#> [3,]    1    0    0    0    0
#> [4,]    0    0    0    0    1
#> [5,]    0    0    1    0    0
#> 
#> [[13]]
#>      [,1] [,2] [,3] [,4] [,5]
#> [1,]    0    0    0    0    1
#> [2,]    1    0    0    0    0
#> [3,]    0    0    0    1    0
#> [4,]    0    0    1    0    0
#> [5,]    0    1    0    0    0
#> 
#> [[14]]
#>      [,1] [,2] [,3] [,4] [,5]
#> [1,]    0    1    0    0    0
#> [2,]    0    0    0    0    1
#> [3,]    0    0    1    0    0
#> [4,]    1    0    0    0    0
#> [5,]    0    0    0    1    0
#> 
#> [[15]]
#>      [,1] [,2] [,3] [,4] [,5]
#> [1,]    0    0    0    1    0
#> [2,]    0    0    0    0    1
#> [3,]    0    0    1    0    0
#> [4,]    0    1    0    0    0
#> [5,]    1    0    0    0    0
#> 
#> [[16]]
#>      [,1] [,2] [,3] [,4] [,5]
#> [1,]    0    0    0    1    0
#> [2,]    0    0    0    0    1
#> [3,]    0    1    0    0    0
#> [4,]    0    0    1    0    0
#> [5,]    1    0    0    0    0
#> 
#> [[17]]
#>      [,1] [,2] [,3] [,4] [,5]
#> [1,]    0    1    0    0    0
#> [2,]    0    0    0    1    0
#> [3,]    0    0    0    0    1
#> [4,]    0    0    1    0    0
#> [5,]    1    0    0    0    0
#> 
#> [[18]]
#>      [,1] [,2] [,3] [,4] [,5]
#> [1,]    0    0    1    0    0
#> [2,]    0    0    0    1    0
#> [3,]    0    1    0    0    0
#> [4,]    1    0    0    0    0
#> [5,]    0    0    0    0    1
#> 
#> [[19]]
#>      [,1] [,2] [,3] [,4] [,5]
#> [1,]    0    0    0    1    0
#> [2,]    1    0    0    0    0
#> [3,]    0    1    0    0    0
#> [4,]    0    0    0    0    1
#> [5,]    0    0    1    0    0
#> 
#> [[20]]
#>      [,1] [,2] [,3] [,4] [,5]
#> [1,]    0    1    0    0    0
#> [2,]    0    0    0    1    0
#> [3,]    0    0    1    0    0
#> [4,]    1    0    0    0    0
#> [5,]    0    0    0    0    1
#> 
#> [[21]]
#>      [,1] [,2] [,3] [,4] [,5]
#> [1,]    0    0    0    0    1
#> [2,]    0    0    1    0    0
#> [3,]    0    0    0    1    0
#> [4,]    0    1    0    0    0
#> [5,]    1    0    0    0    0
#> 
#> [[22]]
#>      [,1] [,2] [,3] [,4] [,5]
#> [1,]    0    0    0    0    1
#> [2,]    0    0    0    1    0
#> [3,]    0    1    0    0    0
#> [4,]    1    0    0    0    0
#> [5,]    0    0    1    0    0
#> 
#> [[23]]
#>      [,1] [,2] [,3] [,4] [,5]
#> [1,]    0    1    0    0    0
#> [2,]    1    0    0    0    0
#> [3,]    0    0    0    0    1
#> [4,]    0    0    1    0    0
#> [5,]    0    0    0    1    0
#> 
#> [[24]]
#>      [,1] [,2] [,3] [,4] [,5]
#> [1,]    0    1    0    0    0
#> [2,]    1    0    0    0    0
#> [3,]    0    0    1    0    0
#> [4,]    0    0    0    1    0
#> [5,]    0    0    0    0    1
#> 
#> [[25]]
#>      [,1] [,2] [,3] [,4] [,5]
#> [1,]    0    0    0    0    1
#> [2,]    1    0    0    0    0
#> [3,]    0    0    1    0    0
#> [4,]    0    1    0    0    0
#> [5,]    0    0    0    1    0
#> 
#> [[26]]
#>      [,1] [,2] [,3] [,4] [,5]
#> [1,]    0    0    1    0    0
#> [2,]    0    0    0    0    1
#> [3,]    1    0    0    0    0
#> [4,]    0    0    0    1    0
#> [5,]    0    1    0    0    0
#> 
#> [[27]]
#>      [,1] [,2] [,3] [,4] [,5]
#> [1,]    0    0    1    0    0
#> [2,]    0    0    0    1    0
#> [3,]    0    1    0    0    0
#> [4,]    0    0    0    0    1
#> [5,]    1    0    0    0    0
#> 
#> [[28]]
#>      [,1] [,2] [,3] [,4] [,5]
#> [1,]    0    1    0    0    0
#> [2,]    1    0    0    0    0
#> [3,]    0    0    0    1    0
#> [4,]    0    0    1    0    0
#> [5,]    0    0    0    0    1
#> 
#> [[29]]
#>      [,1] [,2] [,3] [,4] [,5]
#> [1,]    1    0    0    0    0
#> [2,]    0    1    0    0    0
#> [3,]    0    0    0    0    1
#> [4,]    0    0    1    0    0
#> [5,]    0    0    0    1    0
#> 
#> [[30]]
#>      [,1] [,2] [,3] [,4] [,5]
#> [1,]    1    0    0    0    0
#> [2,]    0    0    0    0    1
#> [3,]    0    0    1    0    0
#> [4,]    0    0    0    1    0
#> [5,]    0    1    0    0    0
#> 
#> [[31]]
#>      [,1] [,2] [,3] [,4] [,5]
#> [1,]    0    0    0    1    0
#> [2,]    0    0    1    0    0
#> [3,]    0    1    0    0    0
#> [4,]    0    0    0    0    1
#> [5,]    1    0    0    0    0
#> 
#> [[32]]
#>      [,1] [,2] [,3] [,4] [,5]
#> [1,]    0    1    0    0    0
#> [2,]    0    0    1    0    0
#> [3,]    0    0    0    1    0
#> [4,]    0    0    0    0    1
#> [5,]    1    0    0    0    0
#> 
#> [[33]]
#>      [,1] [,2] [,3] [,4] [,5]
#> [1,]    0    0    0    1    0
#> [2,]    0    0    0    0    1
#> [3,]    0    0    1    0    0
#> [4,]    1    0    0    0    0
#> [5,]    0    1    0    0    0
#> 
#> [[34]]
#>      [,1] [,2] [,3] [,4] [,5]
#> [1,]    0    1    0    0    0
#> [2,]    0    0    1    0    0
#> [3,]    0    0    0    0    1
#> [4,]    1    0    0    0    0
#> [5,]    0    0    0    1    0
#> 
#> [[35]]
#>      [,1] [,2] [,3] [,4] [,5]
#> [1,]    1    0    0    0    0
#> [2,]    0    0    0    0    1
#> [3,]    0    0    0    1    0
#> [4,]    0    1    0    0    0
#> [5,]    0    0    1    0    0
#> 
#> [[36]]
#>      [,1] [,2] [,3] [,4] [,5]
#> [1,]    0    0    1    0    0
#> [2,]    1    0    0    0    0
#> [3,]    0    1    0    0    0
#> [4,]    0    0    0    0    1
#> [5,]    0    0    0    1    0
#> 
#> [[37]]
#>      [,1] [,2] [,3] [,4] [,5]
#> [1,]    0    1    0    0    0
#> [2,]    0    0    0    1    0
#> [3,]    0    0    1    0    0
#> [4,]    0    0    0    0    1
#> [5,]    1    0    0    0    0
#> 
#> [[38]]
#>      [,1] [,2] [,3] [,4] [,5]
#> [1,]    0    1    0    0    0
#> [2,]    0    0    0    0    1
#> [3,]    1    0    0    0    0
#> [4,]    0    0    1    0    0
#> [5,]    0    0    0    1    0
#> 
#> [[39]]
#>      [,1] [,2] [,3] [,4] [,5]
#> [1,]    1    0    0    0    0
#> [2,]    0    0    0    1    0
#> [3,]    0    0    0    0    1
#> [4,]    0    0    1    0    0
#> [5,]    0    1    0    0    0
#> 
#> [[40]]
#>      [,1] [,2] [,3] [,4] [,5]
#> [1,]    0    0    1    0    0
#> [2,]    1    0    0    0    0
#> [3,]    0    0    0    0    1
#> [4,]    0    0    0    1    0
#> [5,]    0    1    0    0    0
#> 
#> [[41]]
#>      [,1] [,2] [,3] [,4] [,5]
#> [1,]    0    1    0    0    0
#> [2,]    0    0    1    0    0
#> [3,]    1    0    0    0    0
#> [4,]    0    0    0    1    0
#> [5,]    0    0    0    0    1
#> 
#> [[42]]
#>      [,1] [,2] [,3] [,4] [,5]
#> [1,]    0    1    0    0    0
#> [2,]    0    0    1    0    0
#> [3,]    0    0    0    0    1
#> [4,]    0    0    0    1    0
#> [5,]    1    0    0    0    0
#> 
#> [[43]]
#>      [,1] [,2] [,3] [,4] [,5]
#> [1,]    1    0    0    0    0
#> [2,]    0    0    0    1    0
#> [3,]    0    0    1    0    0
#> [4,]    0    0    0    0    1
#> [5,]    0    1    0    0    0
#> 
#> [[44]]
#>      [,1] [,2] [,3] [,4] [,5]
#> [1,]    1    0    0    0    0
#> [2,]    0    0    0    1    0
#> [3,]    0    0    1    0    0
#> [4,]    0    1    0    0    0
#> [5,]    0    0    0    0    1
#> 
#> [[45]]
#>      [,1] [,2] [,3] [,4] [,5]
#> [1,]    0    0    0    0    1
#> [2,]    0    0    1    0    0
#> [3,]    0    1    0    0    0
#> [4,]    0    0    0    1    0
#> [5,]    1    0    0    0    0
#> 
#> [[46]]
#>      [,1] [,2] [,3] [,4] [,5]
#> [1,]    0    0    0    1    0
#> [2,]    0    0    0    0    1
#> [3,]    0    1    0    0    0
#> [4,]    1    0    0    0    0
#> [5,]    0    0    1    0    0
#> 
#> [[47]]
#>      [,1] [,2] [,3] [,4] [,5]
#> [1,]    1    0    0    0    0
#> [2,]    0    0    1    0    0
#> [3,]    0    0    0    0    1
#> [4,]    0    1    0    0    0
#> [5,]    0    0    0    1    0
#> 
#> [[48]]
#>      [,1] [,2] [,3] [,4] [,5]
#> [1,]    0    1    0    0    0
#> [2,]    1    0    0    0    0
#> [3,]    0    0    0    1    0
#> [4,]    0    0    0    0    1
#> [5,]    0    0    1    0    0
#> 
#> [[49]]
#>      [,1] [,2] [,3] [,4] [,5]
#> [1,]    1    0    0    0    0
#> [2,]    0    0    1    0    0
#> [3,]    0    0    0    1    0
#> [4,]    0    1    0    0    0
#> [5,]    0    0    0    0    1
#> 
#> [[50]]
#>      [,1] [,2] [,3] [,4] [,5]
#> [1,]    1    0    0    0    0
#> [2,]    0    0    1    0    0
#> [3,]    0    0    0    0    1
#> [4,]    0    0    0    1    0
#> [5,]    0    1    0    0    0
#> 
#> [[51]]
#>      [,1] [,2] [,3] [,4] [,5]
#> [1,]    0    0    1    0    0
#> [2,]    0    1    0    0    0
#> [3,]    0    0    0    0    1
#> [4,]    1    0    0    0    0
#> [5,]    0    0    0    1    0
#> 
#> [[52]]
#>      [,1] [,2] [,3] [,4] [,5]
#> [1,]    0    1    0    0    0
#> [2,]    0    0    0    1    0
#> [3,]    0    0    0    0    1
#> [4,]    1    0    0    0    0
#> [5,]    0    0    1    0    0
#> 
#> [[53]]
#>      [,1] [,2] [,3] [,4] [,5]
#> [1,]    0    0    1    0    0
#> [2,]    0    1    0    0    0
#> [3,]    0    0    0    1    0
#> [4,]    0    0    0    0    1
#> [5,]    1    0    0    0    0
#> 
#> [[54]]
#>      [,1] [,2] [,3] [,4] [,5]
#> [1,]    0    0    1    0    0
#> [2,]    0    1    0    0    0
#> [3,]    1    0    0    0    0
#> [4,]    0    0    0    0    1
#> [5,]    0    0    0    1    0
#> 
#> [[55]]
#>      [,1] [,2] [,3] [,4] [,5]
#> [1,]    0    0    1    0    0
#> [2,]    0    1    0    0    0
#> [3,]    1    0    0    0    0
#> [4,]    0    0    0    1    0
#> [5,]    0    0    0    0    1
#> 
#> [[56]]
#>      [,1] [,2] [,3] [,4] [,5]
#> [1,]    0    0    0    1    0
#> [2,]    1    0    0    0    0
#> [3,]    0    0    1    0    0
#> [4,]    0    0    0    0    1
#> [5,]    0    1    0    0    0
#> 
#> [[57]]
#>      [,1] [,2] [,3] [,4] [,5]
#> [1,]    0    0    1    0    0
#> [2,]    1    0    0    0    0
#> [3,]    0    1    0    0    0
#> [4,]    0    0    0    1    0
#> [5,]    0    0    0    0    1
#> 
#> [[58]]
#>      [,1] [,2] [,3] [,4] [,5]
#> [1,]    0    0    0    0    1
#> [2,]    0    1    0    0    0
#> [3,]    0    0    1    0    0
#> [4,]    0    0    0    1    0
#> [5,]    1    0    0    0    0
#> 
#> [[59]]
#>      [,1] [,2] [,3] [,4] [,5]
#> [1,]    1    0    0    0    0
#> [2,]    0    0    0    1    0
#> [3,]    0    1    0    0    0
#> [4,]    0    0    1    0    0
#> [5,]    0    0    0    0    1
#> 
#> [[60]]
#>      [,1] [,2] [,3] [,4] [,5]
#> [1,]    1    0    0    0    0
#> [2,]    0    1    0    0    0
#> [3,]    0    0    1    0    0
#> [4,]    0    0    0    0    1
#> [5,]    0    0    0    1    0
#> 
#> [[61]]
#>      [,1] [,2] [,3] [,4] [,5]
#> [1,]    0    0    0    0    1
#> [2,]    0    0    0    1    0
#> [3,]    0    0    1    0    0
#> [4,]    1    0    0    0    0
#> [5,]    0    1    0    0    0
#> 
#> [[62]]
#>      [,1] [,2] [,3] [,4] [,5]
#> [1,]    0    0    0    1    0
#> [2,]    1    0    0    0    0
#> [3,]    0    1    0    0    0
#> [4,]    0    0    1    0    0
#> [5,]    0    0    0    0    1
#> 
#> [[63]]
#>      [,1] [,2] [,3] [,4] [,5]
#> [1,]    1    0    0    0    0
#> [2,]    0    1    0    0    0
#> [3,]    0    0    0    1    0
#> [4,]    0    0    1    0    0
#> [5,]    0    0    0    0    1
#> 
#> [[64]]
#>      [,1] [,2] [,3] [,4] [,5]
#> [1,]    0    0    0    1    0
#> [2,]    0    0    1    0    0
#> [3,]    0    1    0    0    0
#> [4,]    1    0    0    0    0
#> [5,]    0    0    0    0    1
#> 
#> [[65]]
#>      [,1] [,2] [,3] [,4] [,5]
#> [1,]    0    0    0    0    1
#> [2,]    0    1    0    0    0
#> [3,]    0    0    0    1    0
#> [4,]    1    0    0    0    0
#> [5,]    0    0    1    0    0
#> 
#> [[66]]
#>      [,1] [,2] [,3] [,4] [,5]
#> [1,]    0    0    0    0    1
#> [2,]    1    0    0    0    0
#> [3,]    0    1    0    0    0
#> [4,]    0    0    0    1    0
#> [5,]    0    0    1    0    0
#> 
#> [[67]]
#>      [,1] [,2] [,3] [,4] [,5]
#> [1,]    0    0    0    1    0
#> [2,]    0    0    0    0    1
#> [3,]    1    0    0    0    0
#> [4,]    0    0    1    0    0
#> [5,]    0    1    0    0    0
#> 
#> [[68]]
#>      [,1] [,2] [,3] [,4] [,5]
#> [1,]    0    0    0    0    1
#> [2,]    0    0    0    1    0
#> [3,]    0    0    1    0    0
#> [4,]    0    1    0    0    0
#> [5,]    1    0    0    0    0
#> 
#> [[69]]
#>      [,1] [,2] [,3] [,4] [,5]
#> [1,]    0    1    0    0    0
#> [2,]    0    0    1    0    0
#> [3,]    0    0    0    1    0
#> [4,]    1    0    0    0    0
#> [5,]    0    0    0    0    1
#> 
#> [[70]]
#>      [,1] [,2] [,3] [,4] [,5]
#> [1,]    0    1    0    0    0
#> [2,]    0    0    0    0    1
#> [3,]    1    0    0    0    0
#> [4,]    0    0    0    1    0
#> [5,]    0    0    1    0    0
#> 
#> [[71]]
#>      [,1] [,2] [,3] [,4] [,5]
#> [1,]    0    0    1    0    0
#> [2,]    1    0    0    0    0
#> [3,]    0    0    0    1    0
#> [4,]    0    0    0    0    1
#> [5,]    0    1    0    0    0
#> 
#> [[72]]
#>      [,1] [,2] [,3] [,4] [,5]
#> [1,]    0    0    0    0    1
#> [2,]    1    0    0    0    0
#> [3,]    0    1    0    0    0
#> [4,]    0    0    1    0    0
#> [5,]    0    0    0    1    0
#> 
#> [[73]]
#>      [,1] [,2] [,3] [,4] [,5]
#> [1,]    0    0    1    0    0
#> [2,]    0    0    0    0    1
#> [3,]    0    0    0    1    0
#> [4,]    0    1    0    0    0
#> [5,]    1    0    0    0    0
#> 
#> [[74]]
#>      [,1] [,2] [,3] [,4] [,5]
#> [1,]    0    0    0    1    0
#> [2,]    0    0    1    0    0
#> [3,]    0    0    0    0    1
#> [4,]    0    1    0    0    0
#> [5,]    1    0    0    0    0
#> 
#> [[75]]
#>      [,1] [,2] [,3] [,4] [,5]
#> [1,]    0    0    0    1    0
#> [2,]    0    1    0    0    0
#> [3,]    0    0    0    0    1
#> [4,]    1    0    0    0    0
#> [5,]    0    0    1    0    0
#> 
#> [[76]]
#>      [,1] [,2] [,3] [,4] [,5]
#> [1,]    1    0    0    0    0
#> [2,]    0    0    0    1    0
#> [3,]    0    0    0    0    1
#> [4,]    0    1    0    0    0
#> [5,]    0    0    1    0    0
#> 
#> [[77]]
#>      [,1] [,2] [,3] [,4] [,5]
#> [1,]    0    0    0    0    1
#> [2,]    0    0    1    0    0
#> [3,]    0    1    0    0    0
#> [4,]    1    0    0    0    0
#> [5,]    0    0    0    1    0
#> 
#> [[78]]
#>      [,1] [,2] [,3] [,4] [,5]
#> [1,]    0    0    1    0    0
#> [2,]    0    1    0    0    0
#> [3,]    0    0    0    0    1
#> [4,]    0    0    0    1    0
#> [5,]    1    0    0    0    0
#> 
#> [[79]]
#>      [,1] [,2] [,3] [,4] [,5]
#> [1,]    0    0    0    0    1
#> [2,]    1    0    0    0    0
#> [3,]    0    0    1    0    0
#> [4,]    0    0    0    1    0
#> [5,]    0    1    0    0    0
#> 
#> [[80]]
#>      [,1] [,2] [,3] [,4] [,5]
#> [1,]    0    0    1    0    0
#> [2,]    0    0    0    1    0
#> [3,]    0    0    0    0    1
#> [4,]    1    0    0    0    0
#> [5,]    0    1    0    0    0
#> 
#> [[81]]
#>      [,1] [,2] [,3] [,4] [,5]
#> [1,]    0    1    0    0    0
#> [2,]    0    0    0    1    0
#> [3,]    1    0    0    0    0
#> [4,]    0    0    1    0    0
#> [5,]    0    0    0    0    1
#> 
#> [[82]]
#>      [,1] [,2] [,3] [,4] [,5]
#> [1,]    0    1    0    0    0
#> [2,]    1    0    0    0    0
#> [3,]    0    0    0    0    1
#> [4,]    0    0    0    1    0
#> [5,]    0    0    1    0    0
#> 
#> [[83]]
#>      [,1] [,2] [,3] [,4] [,5]
#> [1,]    0    0    0    0    1
#> [2,]    0    0    0    1    0
#> [3,]    1    0    0    0    0
#> [4,]    0    0    1    0    0
#> [5,]    0    1    0    0    0
#> 
#> [[84]]
#>      [,1] [,2] [,3] [,4] [,5]
#> [1,]    0    0    0    0    1
#> [2,]    0    0    1    0    0
#> [3,]    1    0    0    0    0
#> [4,]    0    1    0    0    0
#> [5,]    0    0    0    1    0
#> 
#> [[85]]
#>      [,1] [,2] [,3] [,4] [,5]
#> [1,]    1    0    0    0    0
#> [2,]    0    0    0    0    1
#> [3,]    0    1    0    0    0
#> [4,]    0    0    0    1    0
#> [5,]    0    0    1    0    0
#> 
#> [[86]]
#>      [,1] [,2] [,3] [,4] [,5]
#> [1,]    0    1    0    0    0
#> [2,]    0    0    0    0    1
#> [3,]    0    0    0    1    0
#> [4,]    1    0    0    0    0
#> [5,]    0    0    1    0    0
#> 
#> [[87]]
#>      [,1] [,2] [,3] [,4] [,5]
#> [1,]    0    1    0    0    0
#> [2,]    0    0    0    0    1
#> [3,]    0    0    0    1    0
#> [4,]    0    0    1    0    0
#> [5,]    1    0    0    0    0
#> 
#> [[88]]
#>      [,1] [,2] [,3] [,4] [,5]
#> [1,]    1    0    0    0    0
#> [2,]    0    0    0    0    1
#> [3,]    0    0    1    0    0
#> [4,]    0    1    0    0    0
#> [5,]    0    0    0    1    0
#> 
#> [[89]]
#>      [,1] [,2] [,3] [,4] [,5]
#> [1,]    0    0    0    1    0
#> [2,]    0    1    0    0    0
#> [3,]    1    0    0    0    0
#> [4,]    0    0    0    0    1
#> [5,]    0    0    1    0    0
#> 
#> [[90]]
#>      [,1] [,2] [,3] [,4] [,5]
#> [1,]    0    0    0    0    1
#> [2,]    0    0    0    1    0
#> [3,]    0    1    0    0    0
#> [4,]    0    0    1    0    0
#> [5,]    1    0    0    0    0
#> 
#> [[91]]
#>      [,1] [,2] [,3] [,4] [,5]
#> [1,]    0    0    1    0    0
#> [2,]    0    0    0    0    1
#> [3,]    1    0    0    0    0
#> [4,]    0    1    0    0    0
#> [5,]    0    0    0    1    0
#> 
#> [[92]]
#>      [,1] [,2] [,3] [,4] [,5]
#> [1,]    0    0    1    0    0
#> [2,]    1    0    0    0    0
#> [3,]    0    0    0    0    1
#> [4,]    0    1    0    0    0
#> [5,]    0    0    0    1    0
#> 
#> [[93]]
#>      [,1] [,2] [,3] [,4] [,5]
#> [1,]    0    0    1    0    0
#> [2,]    0    0    0    1    0
#> [3,]    1    0    0    0    0
#> [4,]    0    0    0    0    1
#> [5,]    0    1    0    0    0
#> 
#> [[94]]
#>      [,1] [,2] [,3] [,4] [,5]
#> [1,]    0    0    1    0    0
#> [2,]    0    1    0    0    0
#> [3,]    0    0    0    1    0
#> [4,]    1    0    0    0    0
#> [5,]    0    0    0    0    1
#> 
#> [[95]]
#>      [,1] [,2] [,3] [,4] [,5]
#> [1,]    0    0    1    0    0
#> [2,]    0    0    0    0    1
#> [3,]    0    0    0    1    0
#> [4,]    1    0    0    0    0
#> [5,]    0    1    0    0    0
#> 
#> [[96]]
#>      [,1] [,2] [,3] [,4] [,5]
#> [1,]    1    0    0    0    0
#> [2,]    0    1    0    0    0
#> [3,]    0    0    0    0    1
#> [4,]    0    0    0    1    0
#> [5,]    0    0    1    0    0
#> 
#> [[97]]
#>      [,1] [,2] [,3] [,4] [,5]
#> [1,]    0    0    1    0    0
#> [2,]    0    0    0    0    1
#> [3,]    0    1    0    0    0
#> [4,]    0    0    0    1    0
#> [5,]    1    0    0    0    0
#> 
#> [[98]]
#>      [,1] [,2] [,3] [,4] [,5]
#> [1,]    0    0    1    0    0
#> [2,]    1    0    0    0    0
#> [3,]    0    0    0    1    0
#> [4,]    0    1    0    0    0
#> [5,]    0    0    0    0    1
#> 
#> [[99]]
#>      [,1] [,2] [,3] [,4] [,5]
#> [1,]    0    0    0    0    1
#> [2,]    0    1    0    0    0
#> [3,]    1    0    0    0    0
#> [4,]    0    0    0    1    0
#> [5,]    0    0    1    0    0
#> 
#> [[100]]
#>      [,1] [,2] [,3] [,4] [,5]
#> [1,]    0    0    0    0    1
#> [2,]    0    1    0    0    0
#> [3,]    0    0    1    0    0
#> [4,]    1    0    0    0    0
#> [5,]    0    0    0    1    0
#> 
#> [[101]]
#>      [,1] [,2] [,3] [,4] [,5]
#> [1,]    0    0    0    1    0
#> [2,]    0    0    1    0    0
#> [3,]    1    0    0    0    0
#> [4,]    0    0    0    0    1
#> [5,]    0    1    0    0    0
#> 
#> [[102]]
#>      [,1] [,2] [,3] [,4] [,5]
#> [1,]    0    0    0    1    0
#> [2,]    0    1    0    0    0
#> [3,]    0    0    1    0    0
#> [4,]    1    0    0    0    0
#> [5,]    0    0    0    0    1
#> 
#> [[103]]
#>      [,1] [,2] [,3] [,4] [,5]
#> [1,]    1    0    0    0    0
#> [2,]    0    0    1    0    0
#> [3,]    0    1    0    0    0
#> [4,]    0    0    0    1    0
#> [5,]    0    0    0    0    1
#> 
#> [[104]]
#>      [,1] [,2] [,3] [,4] [,5]
#> [1,]    0    0    1    0    0
#> [2,]    0    0    0    1    0
#> [3,]    0    0    0    0    1
#> [4,]    0    1    0    0    0
#> [5,]    1    0    0    0    0
#> 
#> [[105]]
#>      [,1] [,2] [,3] [,4] [,5]
#> [1,]    0    0    0    0    1
#> [2,]    0    0    0    1    0
#> [3,]    1    0    0    0    0
#> [4,]    0    1    0    0    0
#> [5,]    0    0    1    0    0
#> 
#> [[106]]
#>      [,1] [,2] [,3] [,4] [,5]
#> [1,]    0    0    0    1    0
#> [2,]    0    0    1    0    0
#> [3,]    0    0    0    0    1
#> [4,]    1    0    0    0    0
#> [5,]    0    1    0    0    0
#> 
#> [[107]]
#>      [,1] [,2] [,3] [,4] [,5]
#> [1,]    1    0    0    0    0
#> [2,]    0    0    0    1    0
#> [3,]    0    1    0    0    0
#> [4,]    0    0    0    0    1
#> [5,]    0    0    1    0    0
#> 
#> [[108]]
#>      [,1] [,2] [,3] [,4] [,5]
#> [1,]    1    0    0    0    0
#> [2,]    0    1    0    0    0
#> [3,]    0    0    0    1    0
#> [4,]    0    0    0    0    1
#> [5,]    0    0    1    0    0
#> 
#> [[109]]
#>      [,1] [,2] [,3] [,4] [,5]
#> [1,]    0    0    0    0    1
#> [2,]    0    0    1    0    0
#> [3,]    0    0    0    1    0
#> [4,]    1    0    0    0    0
#> [5,]    0    1    0    0    0
#> 
#> [[110]]
#>      [,1] [,2] [,3] [,4] [,5]
#> [1,]    0    0    0    1    0
#> [2,]    1    0    0    0    0
#> [3,]    0    0    0    0    1
#> [4,]    0    0    1    0    0
#> [5,]    0    1    0    0    0
#> 
#> [[111]]
#>      [,1] [,2] [,3] [,4] [,5]
#> [1,]    0    1    0    0    0
#> [2,]    0    0    1    0    0
#> [3,]    1    0    0    0    0
#> [4,]    0    0    0    0    1
#> [5,]    0    0    0    1    0
#> 
#> [[112]]
#>      [,1] [,2] [,3] [,4] [,5]
#> [1,]    0    0    0    0    1
#> [2,]    1    0    0    0    0
#> [3,]    0    0    0    1    0
#> [4,]    0    1    0    0    0
#> [5,]    0    0    1    0    0
#> 
#> [[113]]
#>      [,1] [,2] [,3] [,4] [,5]
#> [1,]    0    0    1    0    0
#> [2,]    0    0    0    1    0
#> [3,]    1    0    0    0    0
#> [4,]    0    1    0    0    0
#> [5,]    0    0    0    0    1
#> 
#> [[114]]
#>      [,1] [,2] [,3] [,4] [,5]
#> [1,]    0    0    0    1    0
#> [2,]    0    0    1    0    0
#> [3,]    1    0    0    0    0
#> [4,]    0    1    0    0    0
#> [5,]    0    0    0    0    1
#> 
#> [[115]]
#>      [,1] [,2] [,3] [,4] [,5]
#> [1,]    1    0    0    0    0
#> [2,]    0    0    0    0    1
#> [3,]    0    0    0    1    0
#> [4,]    0    0    1    0    0
#> [5,]    0    1    0    0    0
#> 
#> [[116]]
#>      [,1] [,2] [,3] [,4] [,5]
#> [1,]    0    0    1    0    0
#> [2,]    0    0    0    0    1
#> [3,]    0    1    0    0    0
#> [4,]    1    0    0    0    0
#> [5,]    0    0    0    1    0
#> 
#> [[117]]
#>      [,1] [,2] [,3] [,4] [,5]
#> [1,]    0    0    0    1    0
#> [2,]    0    1    0    0    0
#> [3,]    1    0    0    0    0
#> [4,]    0    0    1    0    0
#> [5,]    0    0    0    0    1
#> 
#> [[118]]
#>      [,1] [,2] [,3] [,4] [,5]
#> [1,]    0    0    0    0    1
#> [2,]    0    1    0    0    0
#> [3,]    1    0    0    0    0
#> [4,]    0    0    1    0    0
#> [5,]    0    0    0    1    0
#> 
#> [[119]]
#>      [,1] [,2] [,3] [,4] [,5]
#> [1,]    1    0    0    0    0
#> [2,]    0    0    1    0    0
#> [3,]    0    1    0    0    0
#> [4,]    0    0    0    0    1
#> [5,]    0    0    0    1    0
#> 
#> [[120]]
#>      [,1] [,2] [,3] [,4] [,5]
#> [1,]    0    1    0    0    0
#> [2,]    0    0    0    0    1
#> [3,]    0    0    1    0    0
#> [4,]    0    0    0    1    0
#> [5,]    1    0    0    0    0
#>