Outer Product

class fastmat.Outer

Bases: Matrix

The outer product is a special case of the Kronecker product of one-dimensional vectors. For given \(a \in \mathbb{C}^n\) and \(b \in \mathbb{C}^m\) it is defined as

\[x \mapsto a \cdot b^\mathrm{T} \cdot x.\]

It is clear, that this matrix has at most rank \(1\) and as such has a fast transformation.

>>> # import the package
>>> import fastmat as fm
>>> import numpy as np
>>>
>>> # define parameter
>>> n, m = 4, 5
>>> v = np.arange(n)
>>> h = np.arange(m)
>>>
>>> # construct the matrix
>>> M = fm.Outer(v, h)

This yields

\[v = (0,1,2,3,4)^\mathrm{T}\]

\[h = (0,1,2,3,4,5)^\mathrm{T}\]

\[\begin{split}M = \begin{bmatrix} 0 & 0 & 0 & 0 & 0 \\ 0 & 1 & 2 & 3 & 4 \\ 0 & 2 & 4 & 6 & 8 \\ 0 & 3 & 6 & 9 & 12 \end{bmatrix}\end{split}\]

__init__()

Initialize a Outer product matrix instance.

Parameters

arrVnumpy.ndarray

A 1d vector defining the column factors of the resulting matrix.

arrHnumpy.ndarray

A 1d vector defining the row factors of the resulting matrix.

**optionsoptional

Additional keyworded arguments. Supports all optional arguments supported by fastmat.Matrix.

vecH

Return the matrix-defining vector of horizontal defining entries.

(read only)

vecV

Return the matrix-defining vector of vertical defining entries.

(read only)