derivative_matrix

cherab.inversion.derivative.derivative_matrix(grid_shape: tuple[int, int], grid_step: float = 1.0, axis: int = 0, scheme: Literal['forward', 'backward', 'central'] = 'forward', mask: ndarray | None = None) → csc_arraySource

Generate derivative matrix.

This function computes the derivative matrix for a regular orthogonal coordinate grid. The grid points must be equally spaced along the given axis. The numerical scheme is based on the finite difference method of forward, backward, or central difference. The dirichlet boundary condition is applied to the edge of the grid.

Parameters:

grid_shapetuple[int, int]

Shape of the grid (N0, N1), where N0 and N1 are the number of grid points along the axis 0 and 1 respectively.

grid_stepfloat, optional

Grid step size along the user-specified axis, by default 1.0.

axisint, optional

Axis along which the derivative is taken. Default is 0. Choose from 0 or 1.

scheme{“forward”, “backward”, “central”}, optional

Scheme of the derivative. Default is “forward”. Choose from “forward”, “backward”, or “central”.

maskndarray, optional

Mask array. Default is None. If masking a certain grid point, the corresponding row and column is set to False in the mask array.

Returns:

(N, N) scipy.sparse.csc_array

Derivative Compressed Sparse Column matrix, where N is the number of grid points same as grid_shape[0] * grid_shape[1].

Notes

The detailed explanation of the derivative matrix can be found in the theory of the derivative matrix.

Examples

dmat = derivative_matrix((3, 3), 1, axis=0, scheme="forward")
dmat.toarray()
array([[-1.,  0.,  0.,  1.,  0.,  0.,  0.,  0.,  0.],
       [ 0., -1.,  0.,  0.,  1.,  0.,  0.,  0.,  0.],
       [ 0.,  0., -1.,  0.,  0.,  1.,  0.,  0.,  0.],
       [ 0.,  0.,  0., -1.,  0.,  0.,  1.,  0.,  0.],
       [ 0.,  0.,  0.,  0., -1.,  0.,  0.,  1.,  0.],
       [ 0.,  0.,  0.,  0.,  0., -1.,  0.,  0.,  1.],
       [ 0.,  0.,  0.,  0.,  0.,  0., -1.,  0.,  0.],
       [ 0.,  0.,  0.,  0.,  0.,  0.,  0., -1.,  0.],
       [ 0.,  0.,  0.,  0.,  0.,  0.,  0.,  0., -1.]])