Multiplication of a tensor with a tensor given by its diagonal

This is a convenience function for scaling elements of a tensor with different numbers based on their position in the tensor.

diagmul.tensor(X,i=names(D),D,j=i,by=NULL)

Arguments

X

The tensor to be scaled

D

A tensor containing scaling constants

i

numeric of character vector giving the dimensions of X to be used for the product.

j

numeric of character vector giving the dimensions of D to be used for the product.

by

Every operation is parallel for all levels of by in X and/or D.

Value

A tensor with the shape and dimensions as X with entries \(X_{ik}\) scaled by \(D_im\), where \(i\) and \(k\) can represent multi-indices.

Details

Let $$X_{i_1\ldots i_d k_1 \ldots k_d}$$ and $$D_{j_1\ldots j_d}$$ than the result is: $$E_{i_1\ldots i_d k_1 \ldots k_d}=X_{i_1\ldots i_d k_1 \ldots k_d}D_{j_1\ldots j_d}$$

See also

to.tensor

Author

K. Gerald van den Boogaart

Examples

(A <- matrix(rep(1:3,each=3),nrow=3))
#>      [,1] [,2] [,3]
#> [1,]    1    2    3
#> [2,]    1    2    3
#> [3,]    1    2    3
(b <- to.tensor(c(1,1/2,1/3)))
#> [1] 1.0000000 0.5000000 0.3333333
#> attr(,"class")
#> [1] "tensor"
diagmul.tensor(as.tensor(A),2,as.tensor(c(1,1/2,1/3)),1)
#>       I2
#> I1     [,1] [,2] [,3]
#>   [1,]    1    1    1
#>   [2,]    1    1    1
#>   [3,]    1    1    1
#> attr(,"class")
#> [1] "tensor" "matrix"
diagmul.tensor(as.tensor(A),1,as.tensor(c(1,1/2,1/3)),1)
#>       I1
#> I2     [,1] [,2]      [,3]
#>   [1,]    1  0.5 0.3333333
#>   [2,]    2  1.0 0.6666667
#>   [3,]    3  1.5 1.0000000
#> attr(,"class")
#> [1] "tensor" "matrix"
A %*% diag(b)
#>      [,1] [,2] [,3]
#> [1,]    1    1    1
#> [2,]    1    1    1
#> [3,]    1    1    1
diag(b) %*% A
#>           [,1]      [,2] [,3]
#> [1,] 1.0000000 2.0000000  3.0
#> [2,] 0.5000000 1.0000000  1.5
#> [3,] 0.3333333 0.6666667  1.0