pylops.FirstDirectionalDerivative

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

First Directional derivative.

Apply a directional derivative operator to a multi-dimensional array along either a single common axis or different axes for each point of the array.

Note

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

Parameters:
dims : tuple

Number of samples for each dimension.

v : np.ndarray, optional

Single direction (array of size \(n_\text{dims}\)) or group of directions (array of size \([n_\text{dims} \times n_{d_0} \times ... \times n_{d_{n_\text{dims}}}]\))

sampling : tuple, optional

Sampling steps for each direction.

edge : bool, optional

Use reduced order derivative at edges (True) or ignore them (False).

kind : str, optional

Derivative kind (forward, centered, or backward).

dtype : str, optional

Type of elements in input array.

Returns:
ddop : pylops.LinearOperator

First directional derivative linear operator

Notes

The FirstDirectionalDerivative applies a first-order derivative to a multi-dimensional array along the direction defined by the unitary vector \(\mathbf{v}\):

\[df_\mathbf{v} = \nabla f \mathbf{v}\]

or along the directions defined by the unitary vectors \(\mathbf{v}(x, y)\):

\[df_\mathbf{v}(x,y) = \nabla f(x,y) \mathbf{v}(x,y)\]

where we have here considered the 2-dimensional case.

This operator can be easily implemented as the concatenation of the pylops.Gradient operator and the pylops.Diagonal operator with \(\mathbf{v}\) along the main diagonal.

Examples using pylops.FirstDirectionalDerivative