Module `hdlib.arithmetic`

Implementation of the arithmetic operators.

This library also provides the same set of arithmetic functions also accessible as Vector's class methods. However, while the result of calling these functions from a Vector object woule be applied in place, invoking the same functions from the hdlib.arithmetic module would initialize new Vector objects.

Functions

def bind(vector1: Vector, vector2: Vector) ‑> Vector

Bind vectors.

Parameters

vector1 : Vector: The first vector object.
vector2 : Vector: The second vector object.

Returns

Vector: A new vector object as the result of the bind operator on the two input vectors.

Raises

Exception: If vectors have different sizes or different vector types.

Notes

The bind operator has the following properties: (i) invertible (unbind); (ii) it distributes over bundling; (iii) it preserves the distance; (iv) the resulting vector is dissimilar to the input vectors.

Examples

>>> from hdlib.space import Vector
>>> from hdlib.arithmetic import bind
>>> vector1 = Vector(size=10000, vtype="binary")
>>> vector2 = Vector(size=10000, vtype="binary")
>>> vector3 = bind(vector1, vector2)
>>> type(vector3)
<class 'hdlib.space.Vector'>

The bind function returns a new Vector object whose content is computed as the element-wise multiplication of the two input vectors.

>>> vector1 = Vector(size=10000, vtype="binary")
>>> vector2 = Vector(size=10000, vtype="bipolar")
>>> vector3 = bind(vector1, vector2)
Exception: Vector types are not compatible

The vector type of the two input vector is different and thus the binding cannot be performed.

>>> vector1 = Vector(size=10000, vtype="bipolar")
>>> vector2 = Vector(size=15000, vtype="bipolar")
>>> vector3 = bind(vector1, vector2)
Exception: Vectors must have the same size

It also throws an exception in case the size of the two input vectors is not the same.

def bundle(vector1: Vector, vector2: Vector) ‑> Vector

Bundle vectors.

Parameters

vector1 : Vector: The first vector object.
vector2 : Vector: The second vector object.

Returns

Vector: A new vector object as the result of the bundle operator on the two input vectors.

Raises

Exception: If vectors have different sizes or different vector types.

Notes

The bundle operator has the following properties: (i) the resulting vector is similar to the input vectors; (ii) the more vectors are involved in bundling, the harder it is to determine the component vectors; (iii) if several copies of any vector are included in bundling, the resulting vector is closer to the dominant vector than to the other components.

Examples

>>> from hdlib.space import Vector
>>> from hdlib.arithmetic import bundle
>>> vector1 = Vector(size=10000, vtype="binary")
>>> vector2 = Vector(size=10000, vtype="binary")
>>> vector3 = budle(vector1, vector2)
>>> type(vector3)
<class 'hdlib.space.Vector'>

The bundle function returns a new Vector object whose content is computed as the element-wise sum of the two input vectors.

>>> vector1 = Vector(size=10000, vtype="binary")
>>> vector2 = Vector(size=10000, vtype="bipolar")
>>> vector3 = budle(vector1, vector2)
Exception: Vector types are not compatible

The vector type of the two input vector is different and thus the bundling cannot be performed.

>>> vector1 = Vector(size=10000, vtype="bipolar")
>>> vector2 = Vector(size=15000, vtype="bipolar")
>>> vector3 = budle(vector1, vector2)
Exception: Vectors must have the same size

It also throws an exception in case the size of the two input vectors is not the same.

def permute(vector: Vector, rotate_by: int = 1) ‑> Vector

Permute a vector

Parameters

vector : Vector: The input vector object.
rotate_by : int: Rotate the input vector by rotate_by positions (the default is 1).

Returns

Vector: A new vector object as the result of the permute operator on the input vector.

Notes

The permute operator has the following properties: (i) invertible; (ii) it distributes over bundling and any elementwise operation; (iii) it preserves the distance; (iv) the resulting vector is dissimilar to the input vectors.

Examples

>>> from hdlib.space import Vector
>>> from hdlib.arithmetic import permute
>>> vector1 = Vector(size=10000, vtype="binary")
>>> vector2 = permute(vector1, rotate_by=2)
>>> type(vector2)
<class 'hdlib.space.Vector'>

The permute function returns a new Vector object whose content is the same of the input vector rotated by 2 positions.

def subtraction(vector1: Vector, vector2: Vector) ‑> Vector

Subtract two vectors.

Parameters

vector1 : Vector: The first vector object.
vector2 : Vector: The second vector object.

Returns

Vector: A new vector object as the result of the subtraction operator on the two input vectors.

Raises

Exception: If vectors have different sizes or different vector types.

Examples

>>> from hdlib.space import Vector
>>> from hdlib.arithmetic import subtraction
>>> vector1 = Vector(size=10000, vtype="binary")
>>> vector2 = Vector(size=10000, vtype="binary")
>>> vector3 = subtraction(vector1, vector2)
>>> type(vector3)
<class 'hdlib.space.Vector'>

The subtraction function returns a new Vector object whose content is computed as the element-wise subtraction of the two input vectors.

>>> vector1 = Vector(size=10000, vtype="binary")
>>> vector2 = Vector(size=10000, vtype="bipolar")
>>> vector3 = subtraction(vector1, vector2)
Exception: Vector types are not compatible

The vector type of the two input vector is different and thus the subtraction cannot be performed.

>>> vector1 = Vector(size=10000, vtype="bipolar")
>>> vector2 = Vector(size=15000, vtype="bipolar")
>>> vector3 = subtraction(vector1, vector2)
Exception: Vectors must have the same size

It also throws an exception in case the size of the two input vectors is not the same.