Tensor multiplication for the tensor class

Performs a tensor multiplication like tensor(), but with named indices, keeping dimnames, and vectorized.

mul.tensor(X,i=c(),Y,j=i,by=NULL)

Arguments

X

a tensor to be multiplied

i

numeric or character vector specifying the dimension to be used in the multiplication for X

Y

a tensor to be multiplied

j

numeric or character vector specifying the dimension to be used in the multiplication for Y

by

the by dimensions if present and not mentioned in i or j are used as sequence dimensions. tensors in these dimensions are processed in parallel. So in this dimension the product is neither inner nor outer but parallel like a*b, rather than a%*%b or a%o%b. Unmentioned dimensions get an outer product. Mentioned dimensions an inner.

Value

The tensor product of X and Y with respect to the regarding dimensions.

Details

Say $$X_{i_1\ldots i_n h_1 \ldots h_l}$$ and $$Y_{j_1\ldots j_n k_1 \ldots k_m}$$ the the result is: $$E_{h_1\ldots h_l k_1 \ldots k_m}= \sum_{i_1,\ldots,i_n} X_{i_1\ldots i_n h_1 \ldots h_l}Y_{j_1\ldots j_n k_1 \ldots k_m}$$

This is an full outer product with i,j not given and a full inner product product of i=dim(X)

See also

to.tensor, %e%, %r%, diagmul.tensor, einstein.tensor, riemann.tensor, solve.tensor

Author

K. Gerald van den Boogaart

Examples

A <- to.tensor(1:20,c(A=2,B=2,C=5))
B <- to.tensor(1:20,c(D=2,B=2,E=5))
mul.tensor(A,"A",A,"B")
#> Warning: Tensor with duplicated names generated: B  C  A  C  
#> , , 1, 1
#> 
#>       C
#> B      [,1] [,2] [,3] [,4] [,5]
#>   [1,]    7   23   39   55   71
#>   [2,]   15   31   47   63   79
#> 
#> , , 2, 1
#> 
#>       C
#> B      [,1] [,2] [,3] [,4] [,5]
#>   [1,]   10   34   58   82  106
#>   [2,]   22   46   70   94  118
#> 
#> , , 1, 2
#> 
#>       C
#> B      [,1] [,2] [,3] [,4] [,5]
#>   [1,]   19   67  115  163  211
#>   [2,]   43   91  139  187  235
#> 
#> , , 2, 2
#> 
#>       C
#> B      [,1] [,2] [,3] [,4] [,5]
#>   [1,]   22   78  134  190  246
#>   [2,]   50  106  162  218  274
#> 
#> , , 1, 3
#> 
#>       C
#> B      [,1] [,2] [,3] [,4] [,5]
#>   [1,]   31  111  191  271  351
#>   [2,]   71  151  231  311  391
#> 
#> , , 2, 3
#> 
#>       C
#> B      [,1] [,2] [,3] [,4] [,5]
#>   [1,]   34  122  210  298  386
#>   [2,]   78  166  254  342  430
#> 
#> , , 1, 4
#> 
#>       C
#> B      [,1] [,2] [,3] [,4] [,5]
#>   [1,]   43  155  267  379  491
#>   [2,]   99  211  323  435  547
#> 
#> , , 2, 4
#> 
#>       C
#> B      [,1] [,2] [,3] [,4] [,5]
#>   [1,]   46  166  286  406  526
#>   [2,]  106  226  346  466  586
#> 
#> , , 1, 5
#> 
#>       C
#> B      [,1] [,2] [,3] [,4] [,5]
#>   [1,]   55  199  343  487  631
#>   [2,]  127  271  415  559  703
#> 
#> , , 2, 5
#> 
#>       C
#> B      [,1] [,2] [,3] [,4] [,5]
#>   [1,]   58  210  362  514  666
#>   [2,]  134  286  438  590  742
#> 
#> attr(,"class")
#> [1] "tensor"