t_mult {rTensor}

Tensor Multiplication (T-MULT)

Description

Implements T-MULT based on block circulant matrices (Kilmer et al. 2013) for 3-tensors.

Usage

t_mult(x, y)

Arguments

x

a 3-tensor

y

another 3-tensor

Details

Uses the Fast Fourier Transform (FFT) speed up suggested by Kilmer et al. 2013 instead of explicitly constructing the block circulant matrix. For the mathematical details of T-MULT, see Kilmer et al. (2013).

Value

tensor product between x and y

Note

This only works (so far) between 3-Tensors.

References

M. Kilmer, K. Braman, N. Hao, and R. Hoover, "Third-order tensors as operators on matrices: a theoretical and computational framework with applications in imaging". SIAM Journal on Matrix Analysis and Applications 2013.

Examples

tnsr <- new("Tensor",3L,c(3L,4L,5L),data=runif(60))
tnsr2 <- new("Tensor",3L,c(4L,3L,5L),data=runif(60))
t_mult(tnsr, tnsr2)