tensorTransform: Linear Transformation of Tensors from mth Mode
In tensorBSS: Blind Source Separation Methods for Tensor-Valued Observations

Description Usage Arguments Details Value Author(s) Examples

Applies a linear transformation to the mth mode of each individual tensor in an array of tensors.

1	tensorTransform(x, A, m)

`x`	Array of an order at least two with the last dimension corresponding to the sampling units.
`A`	Matrix corresponding to the desired linear transformation with the number of columns equal to the size of the `m`th dimension of `x`.
`m`	The mode from which the linear transform is to be applied.

Applies the linear transformation given by the matrix A of size q_m x p_m to the mth mode of each of the n observed tensors X_i in the given p_1 x p_2 x ... x p_r x n-dimensional array x. This is equivalent to separately applying the linear transformation given by A to each m-mode vector of each X_i.

Array of size p_1 x p_2 x ... x p_(m-1) x q_m x p_(m+1) x ... x p_r x n

Joni Virta

# Generate sample data.
n <- 10
x <- t(cbind(rnorm(n, mean = 0),
             rnorm(n, mean = 1),
             rnorm(n, mean = 2),
             rnorm(n, mean = 3),
             rnorm(n, mean = 4),
             rnorm(n, mean = 5)))

dim(x) <- c(3, 2, n)

# Transform from the second mode
A <- matrix(c(2, 1, 0, 3), 2, 2)
z <- tensorTransform(x, A, 2)

# Compare
z[, , 1]
x[, , 1]%*%t(A)