desc.basis.DoubleFourierSeries.evaluate

DoubleFourierSeries.evaluate(grid, derivatives=array([0, 0, 0]), modes=None)Source

Evaluate basis functions at specified nodes.

Parameters:

• grid (Grid or ndarray of float, size(num_nodes,3)) – Node coordinates, in (rho,theta,zeta).

• derivatives (ndarray of int, shape(num_derivatives,3)) – Order of derivatives to compute in (rho,theta,zeta).

• modes (ndarray of in, shape(num_modes,3), optional) – Basis modes to evaluate (if None, full basis is used).

Returns:

y (ndarray, shape(num_nodes,num_modes)) – Basis functions evaluated at nodes. The Vandermonde matrix when modes is None is given by y.reshape(-1,2*M+1,2*N+1) and is an outer product of Fourier matrices with order [sin(M𝛉), …, sin(𝛉), 1, cos(𝛉), …, cos(M𝛉)] ⊗ [sin(N𝛇), …, sin(𝛇), 1, cos(𝛇), …, cos(N𝛇)].