spectral.FourierEquispacedBasis

class spectral.FourierEquispacedBasis(domain: tuple[float, float] = (0.0, 6.283185307179586), representation: str = 'real')

Bases: SpectralBasis

Equispaced Fourier basis on a periodic interval.

Methods

__init__
diff_matrix	Return Fourier differentiation matrix.
mass_matrix	Return diagonal mass matrix for trapezoidal quadrature.
nodes	Return equispaced nodes on the periodic domain.

diff_matrix(nodes: ndarray) → ndarray

Return Fourier differentiation matrix.

Parameters:

nodesnp.ndarray

Fourier collocation nodes

Returns:

np.ndarray

Fourier differentiation matrix of shape (N, N)

mass_matrix(nodes: ndarray) → ndarray

Return diagonal mass matrix for trapezoidal quadrature.

Parameters:

nodesnp.ndarray

Fourier collocation nodes

Returns:

np.ndarray

Diagonal mass matrix of shape (N, N)

nodes(num_points: int) → ndarray

Return equispaced nodes on the periodic domain.

Parameters:

num_pointsint

Number of equispaced nodes

Returns:

np.ndarray

Equispaced nodes on the periodic interval