The matrix corresponding to a tensor seen as a linear mapping of tensors.

A tensor can be seen as a linear mapping of a tensor to a tensor. This function gives the corresponding matrix of the mapping.

to.matrix.tensor(X,i,j,by=NULL)

Arguments

X

The tensor

i

The image indices of the linear mapping

j

The domain indices of the linear mapping

by

the operation is done in parallel for these dimensions

Value

if no by is given a matrix. Otherwise a tensor of level 2+length(dim(X))[by] giving matrices for each specification of the by dimensions.

Details

A tensor can be seen as a linear mapping of a tensor to a tensor. This function computes the corresponding matrix, mapping the entries of the domain tensor to the entries of the image tensor.

See also

to.tensor, solve.tensor, inv.tensor, svd.tensor

Author

K. Gerald van den Boogaart

Examples

A <- reorder.tensor(to.tensor(1:30,c(a=2,b=3,c=5)),c("c","a","b"))

to.matrix.tensor(A,"a",c("b","c"))              # matrix(1:30,nrow=2)
#>       
#>        [,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8] [,9] [,10] [,11] [,12] [,13]
#>   [1,]    1    3    5    7    9   11   13   15   17    19    21    23    25
#>   [2,]    2    4    6    8   10   12   14   16   18    20    22    24    26
#>       
#>        [,14] [,15]
#>   [1,]    27    29
#>   [2,]    28    30

to.matrix.tensor(A,c("a","b"),c("c"))           # matrix(1:30,nrow=6)
#>       
#>        [,1] [,2] [,3] [,4] [,5]
#>   [1,]    1    7   13   19   25
#>   [2,]    2    8   14   20   26
#>   [3,]    3    9   15   21   27
#>   [4,]    4   10   16   22   28
#>   [5,]    5   11   17   23   29
#>   [6,]    6   12   18   24   30

to.matrix.tensor(A,c("a","b"),by=c("c")) # structure(1:30,dim=c(6,1,5)))
#> , , 1
#> 
#>       
#>        [,1]
#>   [1,]    1
#>   [2,]    2
#>   [3,]    3
#>   [4,]    4
#>   [5,]    5
#>   [6,]    6
#> 
#> , , 2
#> 
#>       
#>        [,1]
#>   [1,]    7
#>   [2,]    8
#>   [3,]    9
#>   [4,]   10
#>   [5,]   11
#>   [6,]   12
#> 
#> , , 3
#> 
#>       
#>        [,1]
#>   [1,]   13
#>   [2,]   14
#>   [3,]   15
#>   [4,]   16
#>   [5,]   17
#>   [6,]   18
#> 
#> , , 4
#> 
#>       
#>        [,1]
#>   [1,]   19
#>   [2,]   20
#>   [3,]   21
#>   [4,]   22
#>   [5,]   23
#>   [6,]   24
#> 
#> , , 5
#> 
#>       
#>        [,1]
#>   [1,]   25
#>   [2,]   26
#>   [3,]   27
#>   [4,]   28
#>   [5,]   29
#>   [6,]   30
#> 
to.matrix.tensor(A,c("a"),by=c("c"))     # structure(1:30,dim=c(2,3,5)))
#> , , 1
#> 
#>       
#>        [,1] [,2] [,3]
#>   [1,]    1    3    5
#>   [2,]    2    4    6
#> 
#> , , 2
#> 
#>       
#>        [,1] [,2] [,3]
#>   [1,]    7    9   11
#>   [2,]    8   10   12
#> 
#> , , 3
#> 
#>       
#>        [,1] [,2] [,3]
#>   [1,]   13   15   17
#>   [2,]   14   16   18
#> 
#> , , 4
#> 
#>       
#>        [,1] [,2] [,3]
#>   [1,]   19   21   23
#>   [2,]   20   22   24
#> 
#> , , 5
#> 
#>       
#>        [,1] [,2] [,3]
#>   [1,]   25   27   29
#>   [2,]   26   28   30
#>