arc_trigonometric_expansion
Bases: transformation
The arc trigonometric data expansion function.
It performs the arc trigonometric expansion of the input vector, and returns the expansion result. The class inherits from the base expansion class (i.e., the transformation class in the module directory).
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Notes
For input vector \(\mathbf{x} \in R^m\), its arc trigonometric expansion can be represented as follows: $$ \begin{equation} \kappa (\mathbf{x}) = \left[ \arccos(\mathbf{x}), \arcsin(\mathbf{x}), \arctan(\mathbf{x}) \right] \in {R}^D, \end{equation} $$ where the output dimensions will be \(D = 3 m\).
By default, the input and output can also be processed with the optional pre- or post-processing functions in the arc trigonometric expansion function.
Attributes:
Name | Type | Description |
---|---|---|
name |
str, default = 'arc_trigonometric_expansion'
|
Name of the expansion function. |
Methods:
Name | Description |
---|---|
__init__ |
It performs the initialization of the expansion function. |
calculate_D |
It calculates the expansion space dimension D based on the input dimension parameter m. |
forward |
It implements the abstract forward method declared in the base expansion class. |
Source code in tinybig/expansion/trigonometric_expansion.py
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__init__(name='arc_trigonometric_expansion', *args, **kwargs)
The initialization method of the arc trigonometric expansion function.
It initializes a arc trigonometric expansion object based on the input function name. This method will also call the initialization method of the base class as well.
Parameters:
Name | Type | Description | Default |
---|---|---|---|
name |
The name of the arc trigonometric expansion function. |
'arc_trigonometric_expansion'
|
Source code in tinybig/expansion/trigonometric_expansion.py
calculate_D(m)
The expansion dimension calculation method.
It calculates the intermediate expansion space dimension based on the input dimension parameter m. For the arc trigonometric expansion function, the expansion space dimension will be $$ D = 3m. $$
Parameters:
Name | Type | Description | Default |
---|---|---|---|
m |
int
|
The dimension of the input space. |
required |
Returns:
Type | Description |
---|---|
int
|
The dimension of the expansion space. |
Source code in tinybig/expansion/trigonometric_expansion.py
forward(x, device='cpu', *args, **kwargs)
The forward method of the data expansion function.
It performs the arc trigonometric data expansion of the input data and returns the expansion result as $$ \begin{equation} \kappa (\mathbf{x}) = \left[ \arccos(\mathbf{x}), \arcsin(\mathbf{x}), \arctan(\mathbf{x}) \right] \in {R}^D. \end{equation} $$
Parameters:
Name | Type | Description | Default |
---|---|---|---|
x |
Tensor
|
The input data vector. |
required |
device |
The device to perform the data expansion. |
'cpu'
|
Returns:
Type | Description |
---|---|
Tensor
|
The expanded data vector of the input. |