Table Of Contents
Table Of Contents

mx.nd.khatri.rao

Description

Computes the Khatri-Rao product of the input matrices.

Given a collection of \(n\) input matrices,

\[A_1 \in \mathbb{R}^{M_1 \times M}, \ldots, A_n \in \mathbb{R}^{M_n \times N},\]

the (column-wise) Khatri-Rao product is defined as the matrix,

\[X = A_1 \otimes \cdots \otimes A_n \in \mathbb{R}^{(M_1 \cdots M_n) \times N},\]

where the \(k\) th column is equal to the column-wise outer product \({A_1}_k \otimes \cdots \otimes {A_n}_k\) where \({A_i}_k\) is the kth column of the ith matrix.

Example:

>>> A = mx.nd.array([[1, -1],
>>>                  [2, -3]])
>>> B = mx.nd.array([[1, 4],
>>>                  [2, 5],
>>>                  [3, 6]])
>>> C = mx.nd.khatri_rao(A, B)
>>> print(C.asnumpy())
[[  1.  -4.]
[  2.  -5.]
[  3.  -6.]
[  2. -12.]
[  4. -15.]
[  6. -18.]]

Arguments

Argument

Description

args

NDArray-or-Symbol[].

Positional input matrices