Creates a Kronecker delta tensor

The delta tensor is the tensor equivalent of the identity.

delta.tensor(d,mark="'",dn=NULL,by=NULL)

Arguments

d

the row dimensions

mark

a character to be concatenated to the names of the row dimensions to get the column dimension names

dn

dimnames for the result

by

the dimensions which should not be duplicated

Value

a tensor with dimension c(d,mark(d,mark))

Details

$$E_{i_1\ldots i_n j_1\ldots j_n}=\delta_{i_1j_1}\ldots\delta_{i_nj_n}$$

See also

to.tensor

Author

K. Gerald van den Boogaart

Examples

delta.tensor(c(a=2,b=3))
#> , , 1, 1
#> 
#>       b
#> a      [,1] [,2] [,3]
#>   [1,]    1    0    0
#>   [2,]    0    0    0
#> 
#> , , 2, 1
#> 
#>       b
#> a      [,1] [,2] [,3]
#>   [1,]    0    0    0
#>   [2,]    1    0    0
#> 
#> , , 1, 2
#> 
#>       b
#> a      [,1] [,2] [,3]
#>   [1,]    0    1    0
#>   [2,]    0    0    0
#> 
#> , , 2, 2
#> 
#>       b
#> a      [,1] [,2] [,3]
#>   [1,]    0    0    0
#>   [2,]    0    1    0
#> 
#> , , 1, 3
#> 
#>       b
#> a      [,1] [,2] [,3]
#>   [1,]    0    0    1
#>   [2,]    0    0    0
#> 
#> , , 2, 3
#> 
#>       b
#> a      [,1] [,2] [,3]
#>   [1,]    0    0    0
#>   [2,]    0    0    1
#> 
#> attr(,"class")
#> [1] "tensor"