tensorBSS (version 0.3.9)

mFlatten: Flattening an Array Along One Mode

Description

Reshapes a higher order array (tensor) into a matrix with a process known as m-mode flattening or matricization.

Usage

mFlatten(x, m)

Value

The \(m\)-mode flattened 3rd order tensor of size \(p_m \times p_1 \cdots p_{m - 1} p_{m + 1} \cdots p_r \times n\).

Arguments

x

an \((r + 1)\)-dimensional array with \(r \geq 2\). The final mode is understood to correspond to the observations (i.e., its length is usually the sample size n).

m

an integer between \(1\) and \(r\) signifying the mode along which the array should be flattened. Note that the flattening cannot be done w.r.t. the final \((r + 1)\)th mode.

Author

Joni Virta

Details

If the original tensor x has the size \(p_1 \times \cdots \times p_r \times n\), then mFlatten(x, m) returns tensor of size \(p_m \times p_1 \cdots p_{m - 1} p_{m + 1} \cdots p_r \times n\) obtained by gathering all \(m\)-mode vectors of x into a wide matrix (an \(m\)-mode vector of x is any vector of length \(p_m\) obtained by varying the \(m\)th index and holding the other indices constant).

Examples

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)

dim(mFlatten(x, 1))
dim(mFlatten(x, 2))