pylops.Gradient(dims, sampling=1, edge=False, dtype='float64', kind='centered')[source]

Apply gradient operator to a multi-dimensional array.

Note

At least 2 dimensions are required, use pylops.FirstDerivative for 1d arrays.

Parameters: dims : tuple Number of samples for each dimension. sampling : tuple, optional Sampling steps for each direction. edge : bool, optional Use reduced order derivative at edges (True) or ignore them (False). dtype : str, optional Type of elements in input array. kind : str, optional Derivative kind (forward, centered, or backward). l2op : pylops.LinearOperator Gradient linear operator

Notes

The Gradient operator applies a first-order derivative to each dimension of a multi-dimensional array in forward mode.

For simplicity, given a three dimensional array, the Gradient in forward mode using a centered stencil can be expressed as:

$\mathbf{g}_{i, j, k} = (f_{i+1, j, k} - f_{i-1, j, k}) / d_1 \mathbf{i_1} + (f_{i, j+1, k} - f_{i, j-1, k}) / d_2 \mathbf{i_2} + (f_{i, j, k+1} - f_{i, j, k-1}) / d_3 \mathbf{i_3}$

which is discretized as follows:

$\begin{split}\mathbf{g} = \begin{bmatrix} \mathbf{df_1} \\ \mathbf{df_2} \\ \mathbf{df_3} \end{bmatrix}\end{split}$