tomatrixtensor: The matrix corresponding to a tensor seen as a linear mapping...

In tensorA: Advanced Tensor Arithmetic with Named Indices

Description

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

Usage

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

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.

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.

Author(s)

K. Gerald van den Boogaart

See Also

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

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)

to.matrix.tensor(A,c("a","b"),c("c"))           # matrix(1:30,nrow=6)

to.matrix.tensor(A,c("a","b"),by=c("c")) # structure(1:30,dim=c(6,1,5)))
to.matrix.tensor(A,c("a"),by=c("c"))     # structure(1:30,dim=c(2,3,5)))

Example output

Attaching package: 'tensorA'

The following object is masked from 'package:base':

    norm

      
       [,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
      
       [,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
, , 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

, , 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

tensorA documentation built on Nov. 20, 2020, 9:07 a.m.