ttl {tensorregress}

Tensor Times List

Description

Contracted (m-Mode) product between a Tensor of arbitrary number of modes and a list of matrices. The result is folded back into Tensor.

Usage

ttl(tnsr, list_mat, ms = NULL)

Arguments

tnsr

Tensor object with K modes

list_mat

a list of matrices

ms

a vector of modes to contract on (order should match the order of list_mat)

Details

Performs ttm repeated for a single Tensor and a list of matrices on multiple modes. For instance, suppose we want to do multiply a Tensor object tnsr with three matrices mat1, mat2, mat3 on modes 1, 2, and 3. We could do ttm(ttm(ttm(tnsr,mat1,1),mat2,2),3), or we could do ttl(tnsr,list(mat1,mat2,mat3),c(1,2,3)). The order of the matrices in the list should obviously match the order of the modes. This is a common operation for various Tensor decompositions such as CP and Tucker. For the math on the m-Mode Product, see Kolda and Bader (2009).

Value

Tensor object with K modes

Note

The returned Tensor does not drop any modes equal to 1.

References

T. Kolda, B. Bader, "Tensor decomposition and applications". SIAM Applied Mathematics and Applications 2009, Vol. 51, No. 3 (September 2009), pp. 455-500. URL: https://www.jstor.org/stable/25662308

See Also

ttm

Examples

tnsr <- new('Tensor',3L,c(3L,4L,5L),data=runif(60))
lizt <- list('mat1' = matrix(runif(30),ncol=3), 
'mat2' = matrix(runif(40),ncol=4),
'mat3' = matrix(runif(50),ncol=5))
ttl(tnsr,lizt,ms=c(1,2,3))