Functions to extract or replace the diagonals of an array, or construct a diagonal array.
diagonal(x = 1, dim = rep(2, 2))
diagonal(x) <- valuean array from which to extract the diagonals, or a vector giving the diagonal values to construct the array.
the dimensions of the (square) array to construct when x is a vector.
vector giving the values of the diagonal entries.
Vector of the diagonal entries of x if x is an array.
If x is a vector, returns the diagonal array with the
entries given by x.
diagonal(x) <- value: set diagonals.
Guidotti E (2022). "calculus: High-Dimensional Numerical and Symbolic Calculus in R." Journal of Statistical Software, 104(5), 1-37. doi:10.18637/jss.v104.i05
Other tensor algebra:
contraction(),
delta(),
einstein(),
epsilon(),
index()
### 3x3 matrix
diagonal(x = 1, dim = c(3,3))
#> [,1] [,2] [,3]
#> [1,] 1 0 0
#> [2,] 0 1 0
#> [3,] 0 0 1
### 2x2x2 array
diagonal(x = 1:2, dim = c(2,2,2))
#> , , 1
#>
#> [,1] [,2]
#> [1,] 1 0
#> [2,] 0 0
#>
#> , , 2
#>
#> [,1] [,2]
#> [1,] 0 0
#> [2,] 0 2
#>
### extract diagonals
x <- diagonal(1:5, dim = c(5,5,5))
diagonal(x)
#> [1] 1 2 3 4 5
### set diagonals
x <- array(0, dim = c(2,2,2))
diagonal(x) <- 1:2
x
#> , , 1
#>
#> [,1] [,2]
#> [1,] 1 0
#> [2,] 0 0
#>
#> , , 2
#>
#> [,1] [,2]
#> [1,] 0 0
#> [2,] 0 2
#>