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

Second Directional derivative.

Apply second directional derivative operator to a multi-dimensional array (at least 2 dimensions are required) along either a single common direction or different directions for each point of the array.

dims : tuple

Number of samples for each dimension.

v : np.ndarray, optional

Single direction (array of size \(n_{dims}\)) or group of directions (array of size \([n_{dims} \times n_{d0} \times ... \times n_{d_{n_{dims}}}]\))

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.

ddop : pylops.LinearOperator

Second directional derivative linear operator


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

\[d^2f_\mathbf{v} = - D_\mathbf{v}^T [D_\mathbf{v} f]\]

where \(D_\mathbf{v}\) is the first-order directional derivative implemented by pylops.SecondDirectionalDerivative.

This operator is sometimes also referred to as directional Laplacian in the literature.

Examples using pylops.SecondDirectionalDerivative