fourier_expansion
Bases: transformation
The fourier data expansion function.
It performs the fourier 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 \(\mathbf{x} \in R^m\), based on the parameters \(P\) and \(N\), its fourier expansion will be $$ \begin{equation} \kappa (\mathbf{x} | P, N) = \left[ \cos (2\pi \frac{1}{P} \mathbf{x} ), \sin(2\pi \frac{1}{P} \mathbf{x} ), \cdots, \cos(2\pi \frac{N}{P} \mathbf{x} ), \sin(2\pi \frac{N}{P} \mathbf{x} ) \right] \in {R}^D, \end{equation} $$ where the output dimension \(D = 2 m N\).
By default, the input and output can also be processed with the optional pre- or post-processing functions in the fourier expansion function.
Attributes:
Name | Type | Description |
---|---|---|
name |
str, default = 'fourier_expansion'
|
Name of the expansion function. |
P |
int, default = 10
|
The period parameter of the expansion. |
N |
int, default = 5
|
The harmonic number of the expansion. |
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/polynomial_expansion.py
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__init__(name='fourier_expansion', P=10, N=5, *args, **kwargs)
The initialization method of fourier expansion function.
It initializes a fourier 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 fourier expansion function. |
'fourier_expansion'
|
|
P |
The period parameter of the expansion. |
10
|
|
N |
The harmonic number of the expansion. |
5
|
Source code in tinybig/expansion/polynomial_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 fourier expansion function, the expansion space dimension is determined by both m and N, which can be represented as:
\[ D = 2 m N. \]
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/polynomial_expansion.py
forward(x, device='cpu', *args, **kwargs)
The forward method of the data expansion function.
It performs the fourier data expansion of the input data and returns the expansion result according to the following equation: $$ \begin{equation} \kappa (\mathbf{x} | P, N) = \left[ \cos (2\pi \frac{1}{P} \mathbf{x} ), \sin(2\pi \frac{1}{P} \mathbf{x} ), \cdots, \cos(2\pi \frac{N}{P} \mathbf{x} ), \sin(2\pi \frac{N}{P} \mathbf{x} ) \right] \in {R}^D, \end{equation} $$
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. |