e3x.nn.functions.trigonometric.basic_fourier

e3x.nn.functions.trigonometric.basic_fourier(x, num, limit=1.0)

Fourier basis functions.

Computes the basis functions

\[\mathrm{fourier}_k(x) = \mathrm{cos}\left(k\cdot\frac{\pi}{l}\cdot x\right)\]

where \(k=0 \dots K-1\) with \(K\) = num and \(l\) = limit.

Plot for \(K = 5\) and \(l = 1\):

Parameters:

• x (<class 'Float[Array, '...']'>) – Input array.

• num (int) – Number of basis functions \(K\).

• limit (Union[Float[Array, ''], float], default: 1.0) – Basis functions most expressive between 0 and limit, see definition above.

Return type:

<class 'Float[Array, '... num']'>

Returns:

Value of all basis functions for all values in x. The output shape follows the input, with an additional dimension of size num appended.