TRES (version 1.1.5)

ttt: Matrix product of two tensors

Description

Matrix product of two tensors unfolded on the specified modes.

Usage

ttt(x, y, ms)

Arguments

x

A tensor instance.

y

A tensor instance.

ms

The indices of the modes to compute on. A single value or a vector.

Value

Return the matrix product of tensors x and y.

Details

Suppose x is a \(s\)-way tensor with dimension \(p_1 \times \ldots \times p_s\) and y is a t-way tensor with dimension \(r_1 \times \ldots \times r_t\). ms specifies the indices on which the tensors x and y are unfolded as columns. Thus, ms must be a subset of 1:min{s,t}. Meanwhile, the sizes of the dimensions specified by ms must match, e.g., if ms = 1:k where k <= min{s,t}, then \(p_1\times \ldots p_k = s_1\times \ldots s_k\). Let \(X_0\) and \(Y_0\) denote the unfolded matrices, the matrix \(X_0 \times Y_0^T\) is returned. See Examples for a better illustration.

Examples

# NOT RUN {
x <- rTensor::as.tensor(array(runif(24), c(3, 4, 2)))
y <- rTensor::as.tensor(array(runif(24), c(3, 4, 2)))
z <- ttt(x, y, 1:2)

# }