tensorTransform2: Linear Transformations of Tensors from Several Modes
In tensorBSS: Blind Source Separation Methods for Tensor-Valued Observations

Description Usage Arguments Details Value Author(s) See Also Examples

Applies a linear transformation to user selected modes of each individual tensor in an array of tensors. The function is a generalization of tensorTransform which only transforms one specific mode.

1	tensorTransform2(x, A, mode, transpose = FALSE)

`x`	Array of order r+1 >= 2 where the last dimension corresponds to the sampling units.
`A`	A list of r matrices to apply linearly to the corresponding mode.
`mode`	subsetting vector indicating which modes should be linearly transformed by multiplying them with the corresponding matrices from `A`.
`transpose`	logical. Should the matrices in `A` be transposed before the mode wise transformations or not.

For the modes i_1,...,i_k, specified via mode, the function applies the linear transformation given by the matrix A^(i_j) of size q_i_j x p_i_j to the i_jth mode of each of the n observed tensors X_i_j in the given p_1 x p_2 x ... x p_r x n-dimensional array x.

Array with r+1 dimensions where the dimensions specfied via mode are transformed.

Klaus Nordhausen

tensorTransform

n <- 5
x <- array(rnorm(5*6*7), dim = c(7, 6, 5))
A1 <- matrix(runif(14), ncol = 7)
A2 <- matrix(rexp(18), ncol = 6)
A  <- list(A1 = A1, A2 = A2)
At <- list(tA1 = t(A1), tA2 = t(A2))

x1 <- tensorTransform2(x, A, 1)
x2 <- tensorTransform2(x, A, -2)
x3 <- tensorTransform(x, A1, 1)
x1 == x2
x1 == x3
x4 <- tensorTransform2(x,At,-2, TRUE)
x1 == x4
x5 <- tensorTransform2(x, A, 1:2)